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Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

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Math Word Problems and Solutions - Distance, Speed, Time

Problem 1 A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon? Click to see solution Solution: Let $x$ be the number of kilograms he sold in the morning.Then in the afternoon he sold $2x$ kilograms. So, the total is $x + 2x = 3x$. This must be equal to 360. $3x = 360$ $x = \frac{360}{3}$ $x = 120$ Therefore, the salesman sold 120 kg in the morning and $2\cdot 120 = 240$ kg in the afternoon.

Problem 2 Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick? Click to see solution Solution: Let $x$ be the amount Peter picked. Then Mary and Lucy picked $2x$ and $x+2$, respectively. So $x+2x+x+2=26$ $4x=24$ $x=6$ Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.

Problem 3 Sophia finished $\frac{2}{3}$ of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book? Click to see solution Solution: Let $x$ be the total number of pages in the book, then she finished $\frac{2}{3}\cdot x$ pages. Then she has $x-\frac{2}{3}\cdot x=\frac{1}{3}\cdot x$ pages left. $\frac{2}{3}\cdot x-\frac{1}{3}\cdot x=90$ $\frac{1}{3}\cdot x=90$ $x=270$ So the book is 270 pages long.

Problem 4 A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs 120 hectares a day. If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days. How many hectares a day would one tractor plough then? Click to see solution Solution: If each of $6$ tractors ploughed $120$ hectares a day and they finished the work in $4$ days, then the whole field is: $120\cdot 6 \cdot 4 = 720 \cdot 4 = 2880$ hectares. Let's suppose that each of the four tractors ploughed $x$ hectares a day. Therefore in 5 days they ploughed $5 \cdot 4 \cdot x = 20 \cdot x$ hectares, which equals the area of the whole field, 2880 hectares. So, we get $20x = 2880$ $ x = \frac{2880}{20} = 144$. Hence, each of the four tractors would plough 144 hectares a day.

Problem 5 A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose? Click to see solution Solution: Let $x$ be the number he chose, then $2\cdot x - 138 = 102$ $2x = 240$ $x = 120$

Problem 6 I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose? Click to see solution Solution: Let $x$ be the number I chose, then $\frac{x}{5}-154=6$ $\frac{x}{5}=160$ $x=800$

Problem 8 One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 18 cm 2 . Find the lengths of all sides. Click to see solution Solution: Let $x$ be the length of the longer side $x \gt 3$, then the other side's length is $x-3$ cm. Then the area is S 1 = x(x - 3) cm 2 . After we increase the lengths of the sides they will become $(x +1)$ and $(x - 3 + 1) = (x - 2)$ cm long. Hence the area of the new rectangle will be $A_2 = (x + 1)\cdot(x - 2)$ cm 2 , which is 18 cm 2 more than the first area. Therefore $A_1 +18 = A_2$ $x(x - 3) + 18 = (x + 1)(x - 2)$ $x^2 - 3x + 18 = x^2 + x - 2x - 2$ $2x = 20$ $x = 10$. So, the sides of the rectangle are $10$ cm and $(10 - 3) = 7$ cm long.

Problem 9 The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from each cow each year? Click to see solution Solution: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced $(8100 - x)$ litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of $15\%$ or $10\%$. So $8100 + \frac{15}{100}\cdot x + \frac{10}{100} \cdot (8100 - x) = 9100$ Therefore $8100 + \frac{3}{20}x + \frac{1}{10}(8100 - x) = 9100$ $\frac{1}{20}x = 190$ $x = 3800$ Therefore, the cows produced 3800 and 4300 litres of milk the first year, and $4370$ and $4730$ litres of milk the second year, respectively.

Problem 10 The distance between stations A and B is 148 km. An express train left station A towards station B with the speed of 80 km/hr. At the same time, a freight train left station B towards station A with the speed of 36 km/hr. They met at station C at 12 pm, and by that time the express train stopped at at intermediate station for 10 min and the freight train stopped for 5 min. Find: a) The distance between stations C and B. b) The time when the freight train left station B. Click to see solution Solution a) Let x be the distance between stations B and C. Then the distance from station C to station A is $(148 - x)$ km. By the time of the meeting at station C, the express train travelled for $\frac{148-x}{80}+\frac{10}{60}$ hours and the freight train travelled for $\frac{x}{36}+\frac{5}{60}$ hours. The trains left at the same time, so: $\frac{148 - x}{80} + \frac{1}{6} = \frac{x}{36} + \frac{1}{12}$. The common denominator for 6, 12, 36, 80 is 720. Then $9(148 - x) +120 = 20x +60$ $1332 - 9x + 120 = 20x + 60$ $29x = 1392$ $x = 48$. Therefore the distance between stations B and C is 48 km. b) By the time of the meeting at station C the freight train rode for $\frac{48}{36} + \frac{5}{60}$ hours, i.e. $1$ hour and $25$ min. Therefore it left station B at $12 - (1 + \frac{25}{60}) = 10 + \frac{35}{60}$ hours, i.e. at 10:35 am.

Problem 11 Susan drives from city A to city B. After two hours of driving she noticed that she covered 80 km and calculated that, if she continued driving at the same speed, she would end up been 15 minutes late. So she increased her speed by 10 km/hr and she arrived at city B 36 minutes earlier than she planned. Find the distance between cities A and B. Click to see solution Solution: Let $x$ be the distance between A and B. Since Susan covered 80 km in 2 hours, her speed was $V = \frac{80}{2} = 40$ km/hr. If she continued at the same speed she would be $15$ minutes late, i.e. the planned time on the road is $\frac{x}{40} - \frac{15}{60}$ hr. The rest of the distance is $(x - 80)$ km. $V = 40 + 10 = 50$ km/hr. So, she covered the distance between A and B in $2 +\frac{x - 80}{50}$ hr, and it was 36 min less than planned. Therefore, the planned time was $2 + \frac{x -80}{50} + \frac{36}{60}$. When we equalize the expressions for the scheduled time, we get the equation: $\frac{x}{40} - \frac{15}{60} = 2 + \frac{x -80}{50} + \frac{36}{60}$ $\frac{x - 10}{40} = \frac{100 + x - 80 + 30}{50}$ $\frac{x - 10}{4} = \frac{x +50}{5}$ $5x - 50 = 4x + 200$ $x = 250$ So, the distance between cities A and B is 250 km.

Problem 12 To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. Click to see solution Solution: Let $x$ be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: $3\cdot 25 + (x - 3)\cdot 30 = 75 + 30(x - 3)$ Therefore: $25 x = 75 + 30(x -3) - 100$ $25x = 75 +30x -90 - 100$ $190 -75 = 30x -25$ $115 = 5x$ $x = 23$ So the company worked 23 days and they made $23\cdot 25+100 = 675$ pieces.

Problem 13 There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted $24$ plants. How many birches and roses were planted? Click to see solution Solution: Let $x$ be the number of roses. Then the number of birches is $24 - x$, and the number of boys is $3\times (24-x)$. If each girl planted 3 roses, there are $\frac{x}{3}$ girls in the class. We know that there are 24 students in the class. Therefore $\frac{x}{3} + 3(24 - x) = 24$ $x + 9(24 - x) = 3\cdot 24$ $x +216 - 9x = 72$ $216 - 72 = 8x$ $\frac{144}{8} = x$ $x = 18$ So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches.

Problem 14 A car left town A towards town B driving at a speed of V = 32 km/hr. After 3 hours on the road the driver stopped for 15 min in town C. Because of a closed road he had to change his route, making the trip 28 km longer. He increased his speed to V = 40 km/hr but still he was 30 min late. Find: a) The distance the car has covered. b) The time that took it to get from C to B. Click to see solution Solution: From the statement of the problem we don't know if the 15 min stop in town C was planned or it was unexpected. So we have to consider both cases. A The stop was planned. Let us consider only the trip from C to B, and let $x$ be the number of hours the driver spent on this trip. Then the distance from C to B is $S = 40\cdot x$ km. If the driver could use the initial route, it would take him $x - \frac{30}{60} = x - \frac{1}{2}$ hours to drive from C to B. The distance from C to B according to the initially itinerary was $(x - \frac{1}{2})\cdot 32$ km, and this distance is $28$ km shorter than $40\cdot x$ km. Then we have the equation $(x - 1/2)\cdot 32 + 28 = 40x$ $32x -16 +28 = 40x$ $-8x = -12$ $8x = 12$ $x = \frac{12}{8}$ $x = 1 \frac{4}{8} = 1 \frac{1}{2} = 1 \frac{30}{60} =$ 1 hr 30 min. So, the car covered the distance between C and B in 1 hour and 30 min. The distance from A to B is $3\cdot 32 + \frac{12}{8}\cdot 40 = 96 + 60 = 156$ km. B Suppose it took $x$ hours for him to get from C to B. Then the distance is $S = 40\cdot x$ km. The driver did not plan the stop at C. Let we accept that he stopped because he had to change the route. It took $x - \frac{30}{60} + \frac{15}{60} = x - \frac{15}{60} = x - \frac{1}{4}$ h to drive from C to B. The distance from C to B is $32(x - \frac{1}{4})$ km, which is $28$ km shorter than $40\cdot x$, i.e. $32(x - \frac{1}{4}) + 28 = 40x$ $32x - 8 +28 = 40x$ $20= 8x$ $x = \frac{20}{8} = \frac{5}{2} = 2 \text{hr } 30 \text{min}.$ The distance covered equals $ 40 \times 2.5 = 100 km$.

Problem 15 If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially? Click to see solution Solution: Let $x$ be the number of days in the initial plan. Therefore, the whole field is $120\cdot x$ hectares. The farmer had to work for $x + 2$ days, and he ploughed $85(x + 2)$ hectares, leaving $40$ hectares unploughed. Then we have the equation: $120x = 85(x + 2) + 40$ $35x = 210$ $x = 6$ So the farmer planned to have the work done in 6 days, and the area of the farm field is $120\cdot 6 = 720$ hectares.

Problem 16 A woodworker normally makes a certain number of parts in 24 days. But he was able to increase his productivity by 5 parts per day, and so he not only finished the job in only 22 days but also he made 80 extra parts. How many parts does the woodworker normally makes per day and how many pieces does he make in 24 days? Click to see solution Solution: Let $x$ be the number of parts the woodworker normally makes daily. In 24 days he makes $24\cdot x$ pieces. His new daily production rate is $x + 5$ pieces and in $22$ days he made $22 \cdot (x + 5)$ parts. This is 80 more than $24\cdot x$. Therefore the equation is: $24\cdot x + 80 = 22(x +5)$ $30 = 2x$ $x = 15$ Normally he makes 15 parts a day and in 24 days he makes $15 \cdot 24 = 360$ parts.

Problem 17 A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker. Click to see solution Solution: Let x km/hr be the initial speed of the biker, then his speed during the second part of the trip is x + 2 km/hr. Half the distance between two cities equals $2\frac{30}{60} \cdot x$ km and $2\frac{20}{60} \cdot (x + 2)$ km. From the equation: $2\frac{30}{60} \cdot x = 2\frac{20}{60} \cdot (x+2)$ we get $x = 28$ km/hr. The intial speed of the biker is 28 km/h. Half the distance between the two towns is $2 h 30 min \times 28 = 2.5 \times 28 = 70$. So the distance is $2 \times 70 = 140$ km.

Problem 18 A train covered half of the distance between stations A and B at the speed of 48 km/hr, but then it had to stop for 15 min. To make up for the delay, it increased its speed by $\frac{5}{3}$ m/sec and it arrived to station B on time. Find the distance between the two stations and the speed of the train after the stop. Click to see solution Solution: First let us determine the speed of the train after the stop. The speed was increased by $\frac{5}{3}$ m/sec $= \frac{5\cdot 60\cdot 60}{\frac{3}{1000}}$ km/hr = $6$ km/hr. Therefore, the new speed is $48 + 6 = 54$ km/hr. If it took $x$ hours to cover the first half of the distance, then it took $x - \frac{15}{60} = x - 0.25$ hr to cover the second part. So the equation is: $48 \cdot x = 54 \cdot (x - 0.25)$ $48 \cdot x = 54 \cdot x - 54\cdot 0.25$ $48 \cdot x - 54 \cdot x = - 13.5$ $-6x = - 13.5$ $x = 2.25$ h. The whole distance is $2 \times 48 \times 2.25 = 216$ km.

Problem 19 Elizabeth can get a certain job done in 15 days, and Tony can finish only 75% of that job within the same time. Tony worked alone for several days and then Elizabeth joined him, so they finished the rest of the job in 6 days, working together. For how many days have each of them worked and what percentage of the job have each of them completed? Click to see solution Solution: First we will find the daily productivity of every worker. If we consider the whole job as unit (1), Elizabeth does $\frac{1}{15}$ of the job per day and Tony does $75\%$ of $\frac{1}{15}$, i.e. $\frac{75}{100}\cdot \frac{1}{15} = \frac{1}{20}$. Suppose that Tony worked alone for $x$ days. Then he finished $\frac{x}{20}$ of the total job alone. Working together for 6 days, the two workers finished $6\cdot (\frac{1}{15}+\frac{1}{20}) = 6\cdot \frac{7}{60} = \frac{7}{10}$ of the job. The sum of $\frac{x}{20}$ and $\frac{7}{10}$ gives us the whole job, i.e. $1$. So we get the equation: $\frac{x}{20}+\frac{7}{10}=1$ $\frac{x}{20} = \frac{3}{10}$ $x = 6$. Tony worked for 6 + 6 = 12 days and Elizabeth worked for $6$ days. The part of job done is $12\cdot \frac{1}{20} = \frac{60}{100} = 60\%$ for Tony, and $6\cdot \frac{1}{15} = \frac{40}{100} = 40\%$ for Elizabeth.

Problem 20 A farmer planned to plough a field by doing 120 hectares a day. After two days of work he increased his daily productivity by 25% and he finished the job two days ahead of schedule. a) What is the area of the field? b) In how many days did the farmer get the job done? c) In how many days did the farmer plan to get the job done? Click to see solution Solution: First of all we will find the new daily productivity of the farmer in hectares per day: 25% of 120 hectares is $\frac{25}{100} \cdot 120 = 30$ hectares, therefore $120 + 30 = 150$ hectares is the new daily productivity. Lets x be the planned number of days allotted for the job. Then the farm is $120\cdot x$ hectares. On the other hand, we get the same area if we add $120 \cdot 2$ hectares to $150(x -4)$ hectares. Then we get the equation $120x = 120\cdot 2 + 150(x -4)$ $x = 12$ So, the job was initially supposed to take 12 days, but actually the field was ploughed in 12 - 2 =10 days. The field's area is $120 \cdot 12 = 1440$ hectares.

Problem 21 To mow a grass field a team of mowers planned to cover 15 hectares a day. After 4 working days they increased the daily productivity by $33 \times \frac{1}{3}\%$, and finished the work 1 day earlier than it was planned. A) What is the area of the grass field? B) How many days did it take to mow the whole field? C) How many days were scheduled initially for this job? Hint : See problem 20 and solve by yourself. Answer: A) 120 hectares; B) 7 days; C) 8 days.

Problem 22 A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minutes ahead of scheduled. If it made 50 km/hr, then by the scheduled time of arrival it would still have 40 km more to go to station B. Find: A) The distance between the two stations; B) The time it takes the train to travel from A to B according to the schedule; C) The speed of the train when it's on schedule. Click to see solution Solution: Let $x$ be the scheduled time for the trip from A to B. Then the distance between A and B can be found in two ways. On one hand, this distance equals $75(x - \frac{48}{60})$ km. On the other hand, it is $50x + 40$ km. So we get the equation: $75(x - \frac{48}{60}) = 50x + 40$ $x = 4$ hr is the scheduled travel time. The distance between the two stations is $50\cdot 4 +40 = 240$ km. Then the speed the train must keep to be on schedule is $\frac{240}{4} = 60$ km/hr.

Problem 23 The distance between towns A and B is 300 km. One train departs from town A and another train departs from town B, both leaving at the same moment of time and heading towards each other. We know that one of them is 10 km/hr faster than the other. Find the speeds of both trains if 2 hours after their departure the distance between them is 40 km. Click to see solution Solution: Let the speed of the slower train be $x$ km/hr. Then the speed of the faster train is $(x + 10)$ km/hr. In 2 hours they cover $2x$ km and $2(x +10)$km, respectively. Therefore if they didn't meet yet, the whole distance from A to B is $2x + 2(x +10) +40 = 4x +60$ km. However, if they already met and continued to move, the distance would be $2x + 2(x + 10) - 40 = 4x - 20$km. So we get the following equations: $4x + 60 = 300$ $4x = 240$ $x = 60$ or $4x - 20 = 300$ $4x = 320$ $x = 80$ Hence the speed of the slower train is $60$ km/hr or $80$ km/hr and the speed of the faster train is $70$ km/hr or $90$ km/hr.

Problem 24 A bus travels from town A to town B. If the bus's speed is 50 km/hr, it will arrive in town B 42 min later than scheduled. If the bus increases its speed by $\frac{50}{9}$ m/sec, it will arrive in town B 30 min earlier than scheduled. Find: A) The distance between the two towns; B) The bus's scheduled time of arrival in B; C) The speed of the bus when it's on schedule. Click to see solution Solution: First we will determine the speed of the bus following its increase. The speed is increased by $\frac{50}{9}$ m/sec $= \frac{50\cdot60\cdot60}{\frac{9}{1000}}$ km/hr $= 20$ km/hr. Therefore, the new speed is $V = 50 + 20 = 70$ km/hr. If $x$ is the number of hours according to the schedule, then at the speed of 50 km/hr the bus travels from A to B within $(x +\frac{42}{60})$ hr. When the speed of the bus is $V = 70$ km/hr, the travel time is $x - \frac{30}{60}$ hr. Then $50(x +\frac{42}{60}) = 70(x-\frac{30}{60})$ $5(x+\frac{7}{10}) = 7(x-\frac{1}{2})$ $\frac{7}{2} + \frac{7}{2} = 7x -5x$ $2x = 7$ $x = \frac{7}{2}$ hr. So, the bus is scheduled to make the trip in $3$ hr $30$ min. The distance between the two towns is $70(\frac{7}{2} - \frac{1}{2}) = 70\cdot 3 = 210$ km and the scheduled speed is $\frac{210}{\frac{7}{2}} = 60$ km/hr.

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Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

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• Multiplication Word Problems One-Step Multiplication Word Problems up to 10 × 10
• Division Word Problems Division Facts Word Problems with Quotients from 5 to 12
• Multi-Step Word Problems Easy Multi-Step Word Problems

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Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

Example: Sam and Alex play tennis.

On the weekend Sam played 4 more games than Alex did, and together they played 12 games.

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

• Read the whole thing first
• Do a sketch if possible
• Assign letters for the values
• Find or work out formulas

You should also write down what is actually being asked for , so you know where you are going and when you have arrived!

Also look for key words:

Thinking Clearly

Some wording can be tricky, making it hard to think "the right way around", such as:

Example: Sam has 2 dollars less than Alex. How do we write this as an equation?

• Let S = dollars Sam has
• Let A = dollars Alex has

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")

Example: on our street there are twice as many dogs as cats. How do we write this as an equation?

• Let D = number of dogs
• Let C = number of cats

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")

Let's start with a really simple example so we see how it's done:

Example: A rectangular garden is 12m by 5m, what is its area ?

Turn the English into Algebra:

• Use w for width of rectangle: w = 12m
• Use h for height of rectangle: h = 5m

Formula for Area of a Rectangle : A = w × h

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

Now let's try the example from the top of the page:

Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?

• Use S for how many games Sam played
• Use A for how many games Alex played

We know that Sam played 4 more games than Alex, so: S = A + 4

And we know that together they played 12 games: S + A = 12

We are being asked for how many games Alex played: A

Which means that Alex played 4 games of tennis.

Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!

A slightly harder example:

Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?

• Use a for Alex's work rate
• Use s for Sam's work rate

12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?

• The number of "5 hour" days: d
• The number of "3 hour" days: e

We know there are seven days in the week, so: d + e = 7

And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27

We are being asked for how many days she trains for 5 hours: d

The number of "5 hour" days is 3

Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.

3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours

Some examples from Geometry:

Example: A circle has an area of 12 mm 2 , what is its radius?

• Use A for Area: A = 12 mm 2
• Use r for radius

And the formula for Area is: A = π r 2

We are being asked for the radius.

We need to rearrange the formula to find the area

Example: A cube has a volume of 125 mm 3 , what is its surface area?

Make a quick sketch:

• Use V for Volume
• Use A for Area
• Use s for side length of cube
• Volume of a cube: V = s 3
• Surface area of a cube: A = 6s 2

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?

• Joel's normal rate of pay: $N per hour
• Joel works for 40 hours at $N per hour = $40N
• When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
• Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
• And together he earned $660, so:

$40N + $(12 × 1¼N) = $660

We are being asked for Joel's normal rate of pay $N.

So Joel’s normal rate of pay is $12 per hour

Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

More about Money, with these two examples involving Compound Interest

Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?

This is the compound interest formula:

So we will use these letters:

• Present Value PV = $2,000
• Interest Rate (as a decimal): r = 0.11
• Number of Periods: n = 3
• Future Value (the value we want): FV

We are being asked for the Future Value: FV

Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?

The compound interest formula:

• Present Value PV = $1,000
• Interest Rate (the value we want): r
• Number of Periods: n = 9
• Future Value: FV = $1,551.33

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33

And an example of a Ratio question:

Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?

• Number of boys now: b
• Number of girls now: g

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1

b + 4 g − 2 = 2 1

Which can be rearranged to b + 4 = 2(g − 2)

We are being asked for how many students there are altogether now: b + g

There are 12 girls !

And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys

So there are now 12 girls and 16 boys in the class, making 28 students altogether .

There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1

And now for some Quadratic Equations :

Example: The product of two consecutive even integers is 168. What are the integers?

Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.

We will call the smaller integer n , and so the larger integer must be n+2

And we are told the product (what we get after multiplying) is 168, so we know:

n(n + 2) = 168

We are being asked for the integers

That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.

Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES

Check 12: 12(12 + 2) = 12×14 = 168 YES

So there are two solutions: −14 and −12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check":

• We could try, say, n=10: 10(12) = 120 NO (too small)
• Next we could try n=12: 12(14) = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).

Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?

Let's first make a sketch so we get things right!:

• the length of the room: L
• the width of the room: W
• the total Area including veranda: A
• the width of the room is half its length: W = ½L
• the total area is the (room width + 3) times the length: A = (W+3) × L = 56

We are being asked for the length of the room: L

This is a quadratic equation , there are many ways to solve it, this time let's use factoring :

And so L = 8 or −14

There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

So the length of the room is 8 m

L = 8, so W = ½L = 4

So the area of the rectangle = (W+3) × L = 7 × 8 = 56

There we are ...

... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?

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Introduction to Word Problems

These lessons, with videos, examples, solutions and worksheets, help Grade 5 students learn how to solve word problems.

Related Pages More Grade 5 Math Word Problems More Lessons for Grade 5 Math Math Worksheets

The following diagram gives some examples of word problems keywords or clue words. Scroll down the page for more examples and solutions of word problems.

Introduction to Word Problem Terms

Problem Solving Strategies

Explain the meanings of the four basic operations–addition, subtraction, multiplication and division–so that you can understand how to solve word problems correctly.

Helpful hints for solving word problems

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Algebra Word Problem Solvers

• Inspiration

Word problems

Here is a list of all of the skills that cover word problems! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

Here is a list of all of the skills that cover word problems! To start practicing, just click on any link.

Pre-K skills

• V.8 Addition word problems with pictures - sums up to 5
• W.8 Addition word problems with pictures - sums up to 10
• X.7 Subtraction word problems with pictures - numbers up to 5
• Y.7 Subtraction word problems with pictures - numbers up to 10

Kindergarten skills

• Q.1 Build cube trains to solve addition word problems - sums up to 5
• Q.2 Addition word problems with pictures - sums up to 5
• Q.3 Write addition sentences for word problems with pictures - sums up to 5
• Q.4 Addition word problems - sums up to 5
• Q.5 Model and write addition sentences for word problems - sums up to 5
• U.1 Build cube trains to solve addition word problems - sums up to 10
• U.2 Addition word problems with pictures - sums up to 10
• U.3 Write addition sentences for word problems with pictures - sums up to 10
• U.4 Addition word problems - sums up to 10
• U.5 Model and write addition sentences for word problems - sums up to 10
• V.4 Subtraction sentences up to 5 - what does the cube train show?
• X.1 Subtraction word problems with pictures - numbers up to 5
• X.2 Write subtraction sentences for word problems with pictures - up to 5
• X.3 Use cube trains to solve subtraction word problems - up to 5
• X.4 Subtraction word problems - numbers up to 5
• X.5 Model and write subtraction sentences for word problems - up to 5
• Y.4 Subtraction sentences up to 10 - what does the cube train show?
• AA.1 Subtraction word problems with pictures - numbers up to 10
• AA.2 Write subtraction sentences for word problems with pictures - up to 10
• AA.3 Use cube trains to solve subtraction word problems - up to 10
• AA.4 Subtraction word problems - numbers up to 10
• AA.5 Model and write subtraction sentences for word problems - up to 10
• CC.1 Addition and subtraction word problems with pictures
• CC.2 Use cube trains to solve addition and subtraction word problems - up to 10
• CC.3 Addition and subtraction word problems
• CC.4 Model and write addition and subtraction sentences for word problems

First-grade skills

• C.6 Skip-counting patterns - with tables
• H.1 Addition word problems with pictures - sums up to 10
• H.2 Write addition sentences for word problems with pictures - sums up to 10
• H.3 Build cube trains to solve addition word problems - sums up to 10
• H.4 Addition word problems - sums up to 10
• H.5 Model and write addition sentences for word problems - sums up to 10
• H.6 Addition sentences for word problems - sums up to 10
• I.5 Subtraction sentences up to 10: what does the cube train show?
• L.1 Subtraction word problems with pictures - up to 10
• L.2 Write subtraction sentences for word problems with pictures - up to 10
• L.3 Use cube trains to solve subtraction word problems - up to 10
• L.4 Subtraction word problems - up to 10
• L.5 Model and write subtraction sentences for word problems - up to 10
• L.6 Subtraction sentences for "take apart" word problems - up to 10
• L.7 Subtraction sentences for word problems - up to 10
• N.1 Comparison word problems up to 10: how many more?
• N.2 Subtraction sentences for comparison word problems up to 10: how many more?
• N.3 Comparison word problems up to 10: how many fewer?
• N.4 Subtraction sentences for comparison word problems up to 10: how many fewer?
• N.5 Comparison word problems up to 10: how many more or fewer?
• N.6 Subtraction sentences for comparison word problems up to 10: how many more or fewer?
• N.7 Comparison word problems up to 10: what is the larger amount?
• N.8 Comparison word problems up to 10: what is the smaller amount?
• N.9 Comparison word problems up to 10
• O.1 Addition and subtraction word problems with pictures - up to 10
• O.2 Use cube trains to solve addition and subtraction word problems - up to 10
• O.3 Word problems with unknown sums and differences - up to 10
• O.4 Addition and subtraction sentences for word problems - up to 10
• O.5 Word problems with change unknown - up to 10
• O.6 Word problems with start unknown - up to 10
• O.7 Word problems with one addend unknown - up to 10
• O.8 Word problems with both addends unknown - up to 10
• O.9 Word problems involving addition and subtraction - up to 10
• O.10 Match word problems to addition and subtraction sentences - up to 10
• R.1 Addition word problems with models - sums up to 20
• R.2 Addition word problems - sums up to 20
• R.3 Addition sentences for word problems - sums up to 20
• R.4 Add three numbers - word problems
• U.1 Subtraction word problems - up to 20
• U.2 Subtraction sentences for word problems - up to 20
• W.1 Comparison word problems up to 20: how many more or fewer?
• W.2 Comparison word problems up to 20: what is the larger amount?
• W.3 Comparison word problems up to 20: what is the smaller amount?
• W.4 Comparison word problems up to 20: part 1
• W.5 Comparison word problems up to 20: part 2
• X.1 Word problems with one addend unknown - up to 20
• X.2 Word problems with both addends unknown - up to 20
• X.3 Use models to solve word problems involving addition and subtraction - up to 20
• X.4 Word problems involving addition and subtraction - up to 20
• X.5 Addition and subtraction sentences for word problems - up to 20
• X.6 Match word problems to addition and subtraction sentences - up to 20
• BB.4 Compare numbers up to 100: word problems
• DD.13 Addition word problems - one-digit plus two-digit numbers
• DD.14 Addition sentences for word problems - one-digit plus two-digit numbers
• EE.11 Customary units of length: word problems
• EE.13 Metric units of length: word problems
• FF.7 Time and clocks: word problems
• HH.8 Money - word problems

Second-grade skills

• B.5 Greatest and least - word problems - up to 100
• B.6 Greatest and least - word problems - up to 1,000
• C.6 Skip-counting stories
• C.10 Skip-counting puzzles
• G.4 Addition word problems - sums to 20
• G.5 Addition sentences for word problems - sums to 20
• G.10 Addition word problems - three one-digit numbers
• G.12 Addition word problems - four or more one-digit numbers
• I.3 Subtraction word problems - up to 20
• I.4 Subtraction sentences for word problems - up to 20
• K.1 Comparison word problems - up to 20
• K.2 Use models to solve addition and subtraction word problems - up to 20
• K.3 Addition and subtraction word problems - up to 20
• K.4 Match word problems to addition and subtraction sentences - up to 20
• K.5 Two-step addition and subtraction word problems - up to 20
• K.6 Solve word problems using guess-and-check - up to 20
• L.16 Guess the number
• N.8 Addition word problems - up to two digits
• N.16 Addition word problems - three numbers up to two digits each
• N.19 Addition word problems - four numbers up to two digits each
• P.10 Subtraction word problems - up to two digits
• R.1 Addition and subtraction word problems - up to 100
• R.2 Two-step addition and subtraction word problems - up to 100
• T.5 Addition word problems - up to three digits
• V.6 Subtraction word problems - up to three digits
• W.4 Addition and subtraction word problems - up to 1,000
• X.6 Solve word problems using repeated addition - sums to 25
• AA.14 Making change
• BB.2 Add money up to $1: word problems
• BB.4 Subtract money up to $1: word problems
• BB.6 Add and subtract money up to $1: word problems
• GG.6 Compare lengths: customary units
• GG.7 Customary units of length: word problems
• HH.4 Compare lengths: metric units
• HH.5 Metric units of length: word problems

Third-grade skills

• A.6 Place value word problems
• A.7 Guess the number
• B.5 Ordering puzzles
• D.3 Estimate sums by rounding: word problems
• E.3 Estimate differences by rounding: word problems
• F.3 Estimate sums and differences: word problems
• G.7 Add two numbers up to three digits: word problems
• G.12 Add three numbers up to three digits each: word problems
• H.7 Subtract numbers up to three digits: word problems
• I.3 Add two numbers up to four digits: word problems
• I.7 Add three numbers up to four digits each: word problems
• J.3 Subtract two numbers up to four digits: word problems
• K.6 Addition and subtraction word problems
• K.7 Age puzzles
• K.8 Find two numbers based on sum and difference
• M.3 Skip-counting puzzles
• S.1 Use equal groups and arrays to solve multiplication word problems
• S.2 Multiplication word problems with factors up to 5
• S.3 Use strip models to solve multiplication word problems
• S.4 Multiplication word problems with factors up to 10
• S.5 Multiplication word problems with factors up to 5: find the missing number
• S.6 Multiplication word problems with factors up to 10: find the missing number
• S.7 Compare numbers using multiplication: word problems
• T.7 Multiply one-digit numbers by two-digit numbers: word problems
• T.9 Multiply three numbers: word problems
• Y.1 Use equal groups to solve division word problems
• Y.2 Use arrays to solve division word problems
• Y.3 Use equal groups and arrays to solve division word problems
• Y.4 Division word problems
• Z.6 Multiplication and division word problems
• AA.4 Addition, subtraction, multiplication, and division word problems
• AA.5 Find two numbers based on sum, difference, product, and quotient
• BB.1 Two-step addition and subtraction word problems
• BB.2 Two-step multiplication and division word problems
• BB.3 Two-step mixed operation word problems
• BB.4 Two-step word problems: identify reasonable answers
• CC.5 Write equations with unknown numbers to represent word problems: multiplication and division only
• CC.6 Write equations with unknown numbers to represent word problems
• FF.1 Unit fractions: modeling word problems
• FF.2 Unit fractions: word problems
• FF.3 Fractions of a whole: modeling word problems
• FF.4 Fractions of a whole: word problems
• FF.5 Fractions of a group: word problems
• KK.5 Compare fractions in recipes
• MM.12 Find the area of rectangles: word problems
• MM.13 Find the missing side length of a rectangle: word problems
• NN.6 Perimeter: word problems
• OO.1 Find the area, perimeter, or side length: word problems
• SS.3 Find the end time: word problems
• SS.4 Find the elapsed time: word problems
• SS.5 Find start and end times: two-step word problems
• UU.6 Measurement word problems
• WW.6 Making change
• WW.10 Add money amounts - word problems

Fourth-grade skills

• A.9 Place value word problems
• B.5 Find the order
• C.5 Rounding puzzles
• D.2 Estimate sums: word problems
• D.4 Add two multi-digit numbers: word problems
• E.2 Estimate differences: word problems
• E.4 Subtract two multi-digit numbers: word problems
• F.8 Compare numbers using multiplication: word problems
• F.9 Comparison word problems: addition or multiplication?
• G.2 Divisibility rules: word problems
• H.4 Estimate products word problems: identify reasonable answers
• H.10 Multiply 1-digit numbers by 2-digit numbers: word problems
• H.11 Multiply 1-digit numbers by 2-digit numbers: multi-step word problems
• H.17 Multiply 1-digit numbers by 3-digit or 4-digit numbers: word problems
• H.18 Multiply 1-digit numbers by 3-digit or 4-digit numbers: multi-step word problems
• I.3 Multiply two multiples of ten: word problems
• I.5 Estimate products: word problems
• I.11 Multiply a 2-digit number by a 2-digit number: word problems
• I.12 Multiply a 2-digit number by a 2-digit number: multi-step word problems
• J.2 Division facts to 10: word problems
• J.4 Division facts to 12: word problems
• L.1 Divide numbers ending in zeros by 1-digit numbers: word problems
• L.2 Divide 2-digit numbers by 1-digit numbers: interpret remainders
• L.3 Divide 2-digit numbers by 1-digit numbers: word problems
• L.4 Divide larger numbers by 1-digit numbers: interpret remainders
• L.5 Divide larger numbers by 1-digit numbers: word problems
• M.2 Estimate sums, differences, products, and quotients: word problems
• M.5 Addition, subtraction, multiplication, and division word problems
• M.7 Find two numbers based on sum and difference
• M.9 Find two numbers based on sum, difference, product, and quotient
• M.11 Write equations to represent word problems
• M.13 Use equations to solve addition and subtraction word problems
• N.1 Multi-step addition and subtraction word problems
• N.2 Multi-step word problems with strip diagrams
• N.3 Use strip diagrams to represent and solve multi-step word problems
• N.4 Multi-step word problems
• N.5 Multi-step word problems involving remainders
• N.6 Multi-step word problems: identify reasonable answers
• N.7 Word problems with extra or missing information
• N.8 Solve word problems using guess-and-check
• O.7 Number patterns: word problems
• P.1 Fractions of a whole: word problems
• P.2 Fractions of a group: word problems
• T.4 Add and subtract fractions with like denominators: word problems
• T.5 Add and subtract fractions with like denominators in recipes
• T.12 Add and subtract mixed numbers with like denominators in recipes
• T.13 Add and subtract mixed numbers with like denominators: word problems
• U.7 Add and subtract fractions with unlike denominators: word problems
• V.6 Multiply unit fractions by whole numbers: word problems
• W.7 Multiply fractions by whole numbers: word problems
• W.10 Multiply fractions and mixed numbers by whole numbers in recipes
• W.13 Fractions of a number: word problems
• Z.7 Add and subtract decimals: word problems
• Z.10 Add 3 or more decimals: word problems
• Z.13 Solve decimal problems using diagrams
• AA.5 Find the change, price, or amount paid
• AA.8 Multi-step word problems with money: addition and subtraction only
• AA.9 Multi-step word problems with money
• CC.5 Elapsed time: word problems
• CC.6 Find start and end times: multi-step word problems
• FF.1 Measurement word problems
• FF.2 Measurement word problems with fractions
• HH.8 Relationship between area and perimeter
• HH.9 Area and perimeter: word problems
• HH.10 Rectangles: relationship between perimeter and area word problems

Fifth-grade skills

• B.2 Estimate sums and differences: word problems
• B.4 Add and subtract whole numbers: word problems
• D.3 Multiply numbers ending in zeros: word problems
• D.6 Estimate products: word problems
• D.8 Multiply by 1-digit numbers: word problems
• D.13 Multiply by 2-digit numbers: word problems
• E.3 Divide numbers ending in zeros: word problems
• E.7 Divide by 1-digit numbers: interpret remainders
• E.8 Divide multi-digit numbers by 1-digit numbers: word problems
• E.12 Divide 2-digit and 3-digit numbers by 2-digit numbers: word problems
• E.14 Divide 4-digit numbers by 2-digit numbers: word problems
• F.5 Divisibility rules: word problems
• G.2 Add, subtract, multiply, and divide whole numbers: word problems
• I.1 Write numerical expressions for word problems
• I.2 Multi-step word problems
• I.3 Multi-step word problems involving remainders
• I.4 Multi-step word problems: identify reasonable answers
• L.7 Add and subtract fractions with unlike denominators: word problems
• L.9 Add 3 or more fractions: word problems
• M.6 Add and subtract mixed numbers: word problems
• M.7 Add and subtract fractions and mixed numbers in recipes
• O.3 Multiply fractions by whole numbers: word problems
• O.6 Fractions of a number: word problems
• P.2 Multiply two fractions: word problems
• R.7 Multiplication with mixed numbers: word problems
• R.8 Multiply fractions and mixed numbers in recipes
• V.2 Add, subtract, multiply, and divide fractions and mixed numbers: word problems
• X.6 Compare, order, and round decimals: word problems
• AA.6 Add and subtract decimals: word problems
• CC.8 Multiply decimals and whole numbers: word problems
• FF.7 Division with decimal quotients: word problems
• GG.2 Add, subtract, multiply, and divide decimals: word problems
• HH.2 Add and subtract money: word problems
• HH.3 Add and subtract money: multi-step word problems
• HH.5 Multiply money amounts: word problems
• HH.6 Multiply money amounts: multi-step word problems
• HH.8 Divide money amounts: word problems
• HH.11 Find the number of each type of coin
• II.10 Multi-step problems with customary unit conversions
• JJ.8 Multi-step problems with metric unit conversions
• JJ.9 Multi-step problems with customary or metric unit conversions
• KK.5 Number patterns: word problems
• MM.2 Write variable expressions: word problems
• MM.4 Write variable equations: word problems
• TT.7 Area and perimeter: word problems
• UU.4 Volume of rectangular prisms made of unit cubes: word problems
• UU.6 Volume of cubes and rectangular prisms: word problems
• UU.7 Compare volumes and dimensions of rectangular prisms: word problems
• VV.1 Income and payroll taxes: understanding pay stubs
• VV.2 Income and payroll taxes: word problems
• VV.3 Sales and property taxes: word problems
• VV.9 Reading financial records
• VV.10 Keeping financial records

Sixth-grade skills

• A.2 Add and subtract whole numbers: word problems
• B.2 Multiply whole numbers: word problems
• B.4 Multiply numbers ending in zeros: word problems
• C.3 Divide numbers ending in zeros: word problems
• E.2 Add, subtract, multiply, or divide two whole numbers: word problems
• E.3 Estimate to solve word problems
• E.4 Multi-step word problems
• E.5 Multi-step word problems: identify reasonable answers
• F.10 GCF and LCM: word problems
• H.2 Add and subtract decimals: word problems
• H.3 Add and subtract money amounts: word problems
• I.6 Divide decimals by whole numbers: word problems
• I.11 Multiply and divide decimals: word problems
• J.2 Add, subtract, multiply, or divide two decimals: word problems
• K.2 Add and subtract fractions with like denominators: word problems
• K.4 Add and subtract fractions with unlike denominators: word problems
• K.7 Add and subtract mixed numbers: word problems
• L.3 Multiply fractions by whole numbers: word problems
• L.7 Multiply fractions: word problems
• L.14 Multiply mixed numbers: word problems
• M.5 Divide fractions by whole numbers in recipes
• M.12 Divide fractions and mixed numbers: word problems
• N.2 Add, subtract, multiply, or divide two fractions: word problems
• O.10 Absolute value and integers: word problems
• P.8 Add and subtract integers: word problems
• Q.6 Compare and order rational numbers: word problems
• S.3 Write a ratio: word problems
• S.8 Equivalent ratios: word problems
• S.11 Calculate speed, distance, or time: word problems
• S.12 Ratios and rates: complete a table and make a graph
• S.13 Use tape diagrams to solve ratio word problems
• S.14 Compare ratios: word problems
• S.15 Compare rates: word problems
• S.16 Ratios and rates: word problems
• S.19 Scale drawings: word problems
• T.3 Identify proportional relationships by graphing
• T.4 Interpret graphs of proportional relationships
• U.5 Convert between percents, fractions, and decimals: word problems
• U.7 Compare percents and fractions: word problems
• V.5 Percents of numbers: word problems
• V.8 Find what percent one number is of another: word problems
• V.11 Solve percent word problems
• W.10 Compare temperatures above and below zero
• X.7 Percents - calculate tax, tip, mark-up, and more
• Y.3 Write variable expressions: word problems
• Y.7 Evaluate variable expressions: word problems
• AA.13 Solve one-step addition and subtraction equations: word problems
• AA.14 Solve one-step multiplication and division equations: word problems
• AA.15 Write a one-step equation: word problems
• AA.16 Solve one-step equations: word problems
• AA.17 Which word problem matches the one-step equation?
• BB.4 Write and graph inequalities: word problems
• CC.2 Identify independent and dependent variables in tables and graphs
• CC.4 Identify independent and dependent variables: word problems
• CC.6 Find a value using two-variable equations: word problems
• CC.7 Solve word problems by finding two-variable equations
• CC.13 Graph a two-variable equation
• CC.14 Interpret a graph: word problems
• GG.17 Area of quadrilaterals and triangles: word problems
• HH.3 Volume of cubes and rectangular prisms: word problems
• JJ.10 Interpret measures of center and variability
• KK.1 Counting principle
• LL.1 Compare checking accounts

Seventh-grade skills

• A.6 Quantities that combine to zero: word problems
• B.14 Add and subtract integers: word problems
• D.2 Add and subtract decimals: word problems
• D.4 Multiply decimals and whole numbers: word problems
• D.6 Divide decimals by whole numbers: word problems
• D.9 Add, subtract, multiply, and divide decimals: word problems
• E.4 GCF and LCM: word problems
• F.1 Understanding fractions: word problems
• F.4 Fractions: word problems with graphs and tables
• F.7 Compare fractions: word problems
• G.2 Add and subtract fractions: word problems
• G.4 Add and subtract mixed numbers: word problems
• G.10 Multiply fractions and mixed numbers: word problems
• G.14 Divide fractions and mixed numbers: word problems
• G.16 Add, subtract, multiply, and divide fractions and mixed numbers: word problems
• I.6 Identify quotients of rational numbers: word problems
• I.11 Multi-step word problems with positive rational numbers
• L.4 Equivalent ratios: word problems
• L.7 Compare ratios: word problems
• L.8 Compare rates: word problems
• L.10 Do the ratios form a proportion: word problems
• L.12 Solve proportions: word problems
• L.13 Estimate population size using proportions
• N.1 Find the constant of proportionality from a table
• N.2 Write equations for proportional relationships from tables
• N.3 Identify proportional relationships by graphing
• N.4 Find the constant of proportionality from a graph
• N.5 Write equations for proportional relationships from graphs
• N.10 Interpret graphs of proportional relationships
• N.11 Write and solve equations for proportional relationships
• O.7 Percents of numbers: word problems
• O.9 Solve percent equations: word problems
• O.11 Percent of change: word problems
• O.12 Percent of change: find the original amount word problems
• O.13 Percent error: word problems
• P.1 Add, subtract, multiply, and divide money amounts: word problems
• P.8 Find the percent: tax, discount, and more
• P.10 Multi-step problems with percents
• R.3 Write variable expressions: word problems
• S.14 Identify equivalent linear expressions: word problems
• T.11 Choose two-step equations: word problems
• T.12 Solve two-step equations: word problems
• U.6 One-step inequalities: word problems
• V.5 Sequences: word problems
• X.1 Identify independent and dependent variables
• X.8 Interpret a graph: word problems
• BB.4 Area and perimeter: word problems
• BB.7 Circles: word problems
• CC.6 Volume of cubes and rectangular prisms: word problems
• DD.2 Scale drawings: word problems
• DD.3 Scale drawings: scale factor word problems
• HH.9 Make inferences from multiple samples
• HH.10 Compare populations using measures of center and spread
• II.4 Experimental probability
• II.10 Find the number of outcomes: word problems

Eighth-grade skills

• A.6 Add and subtract integers: word problems
• B.7 Add and subtract rational numbers: word problems
• B.10 Multiply and divide rational numbers: word problems
• B.14 Multi-step word problems
• G.2 Solve proportions: word problems
• G.3 Estimate population size using proportions
• G.4 Scale drawings: word problems
• G.5 Scale drawings: scale factor word problems
• H.4 Find what percent one number is of another: word problems
• H.7 Percents of numbers: word problems
• H.11 Percent of change: word problems
• H.12 Percent of change: find the original amount word problems
• I.6 Find the percent: tax, discount, and more
• I.8 Multi-step problems with percents
• K.4 Write variable expressions: word problems
• L.9 Identify equivalent linear expressions: word problems
• M.10 Solve one-step and two-step equations: word problems
• M.14 Solve equations with variables on both sides: word problems
• T.5 Pythagorean theorem: word problems
• V.3 Area and perimeter: word problems
• V.5 Circles: word problems
• X.1 Find the constant of proportionality from a table
• X.2 Write equations for proportional relationships from tables
• X.3 Identify proportional relationships by graphing
• X.4 Find the constant of proportionality from a graph
• X.5 Write equations for proportional relationships from graphs
• X.8 Identify proportional relationships: word problems
• X.9 Graph proportional relationships and find the slope
• X.10 Interpret graphs of proportional relationships
• X.11 Write and solve equations for proportional relationships
• X.12 Compare proportional relationships represented in different ways
• BB.3 Identify independent and dependent variables
• CC.4 Interpret points on the graph of a linear function
• CC.6 Interpret the slope and y-intercept of a linear function
• CC.10 Write linear functions: word problems
• FF.5 Sequences: word problems
• GG.3 Solve a system of equations by graphing: word problems
• GG.9 Solve a system of equations using substitution: word problems
• GG.11 Solve a system of equations using elimination: word problems
• GG.13 Solve a system of equations using any method: word problems
• II.10 Interpret lines of best fit: word problems
• JJ.3 Experimental probability
• JJ.10 Counting principle

Algebra 1 skills

• C.9 Solve one-step and two-step linear equations: word problems
• C.11 Consecutive integer problems
• C.16 Solve linear equations with variables on both sides: word problems
• D.1 Area and perimeter: word problems
• E.1 Scale drawings: word problems
• E.5 Multi-step problems with unit conversions
• E.6 Rate of travel: word problems
• E.7 Weighted averages: word problems
• M.3 Identify independent and dependent variables
• N.4 Evaluate a linear function from its graph: word problems
• N.5 Interpret the slope and y-intercept of a linear function
• N.8 Domain and range of linear functions: word problems
• O.3 Solve a system of equations by graphing: word problems
• O.9 Solve a system of equations using substitution: word problems
• O.11 Solve a system of equations using elimination: word problems
• O.13 Solve a system of equations using augmented matrices: word problems
• O.15 Solve a system of equations using any method: word problems
• P.5 Write two-variable inequalities: word problems
• V.7 Write exponential functions: word problems
• V.8 Exponential growth and decay: word problems
• Z.7 Solve quadratic equations: word problems
• AA.5 Write linear and exponential functions: word problems
• JJ.6 Interpret lines of best fit: word problems
• JJ.8 Interpret regression lines
• JJ.9 Analyze a regression line of a data set
• KK.6 Identify independent and dependent events
• KK.8 Counting principle
• KK.9 Permutations

Geometry skills

• A.1 Identify hypotheses and conclusions
• A.2 Counterexamples
• P.1 Pythagorean theorem
• V.9 Calculate density, mass, and volume
• AA.5 Counting principle
• AA.6 Permutations
• AA.15 Find probabilities using the addition rule

Algebra 2 skills

• B.3 Solve linear equations: word problems
• E.3 Solve a system of equations by graphing: word problems
• E.7 Solve a system of equations using substitution: word problems
• E.9 Solve a system of equations using elimination: word problems
• E.11 Solve a system of equations using any method: word problems
• F.1 Write two-variable linear inequalities: word problems
• O.7 Solve quadratic equations: word problems
• Z.3 Write exponential functions: word problems
• Z.9 Exponential growth and decay: word problems
• CC.4 Compound interest: word problems
• CC.5 Continuously compounded interest: word problems
• OO.2 Counting principle
• OO.4 Find probabilities using combinations and permutations
• OO.5 Find probabilities using two-way frequency tables
• OO.10 Find conditional probabilities using two-way frequency tables
• OO.11 Find probabilities using the addition rule
• PP.8 Write the probability distribution for a game of chance
• PP.9 Expected values for a game of chance
• PP.10 Choose the better bet
• QQ.1 Find probabilities using the binomial distribution
• RR.5 Find confidence intervals for population means
• RR.6 Find confidence intervals for population proportions
• RR.7 Interpret confidence intervals for population means
• RR.8 Experiment design
• RR.9 Analyze the results of an experiment using simulations
• SS.5 Interpret regression lines
• SS.6 Analyze a regression line of a data set
• TT.19 Solve a system of equations using augmented matrices: word problems

Precalculus skills

• D.9 Solve quadratic equations: word problems
• K.5 Exponential growth and decay: word problems
• K.6 Compound interest: word problems
• N.2 Solve a system of equations by graphing: word problems
• N.5 Solve a system of equations using substitution: word problems
• N.7 Solve a system of equations using elimination: word problems
• N.9 Solve a system of equations using augmented matrices: word problems
• CC.3 Find probabilities using combinations and permutations
• CC.4 Find probabilities using two-way frequency tables
• CC.8 Find conditional probabilities using two-way frequency tables
• CC.9 Find probabilities using the addition rule
• DD.8 Write the probability distribution for a game of chance
• DD.9 Expected values for a game of chance
• DD.10 Choose the better bet
• EE.1 Find probabilities using the binomial distribution
• EE.2 Mean, variance, and standard deviation of binomial distributions
• EE.9 Use normal distributions to approximate binomial distributions
• FF.5 Find confidence intervals for population means
• FF.6 Find confidence intervals for population proportions
• FF.7 Interpret confidence intervals for population means
• FF.8 Experiment design
• FF.9 Analyze the results of an experiment using simulations
• GG.5 Interpret regression lines
• GG.6 Analyze a regression line of a data set
• GG.7 Analyze a regression line using statistics of a data set

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Praxis Core Math

Course: praxis core math   >   unit 1.

• Algebraic properties | Lesson
• Algebraic properties | Worked example
• Solution procedures | Lesson
• Solution procedures | Worked example
• Equivalent expressions | Lesson
• Equivalent expressions | Worked example
• Creating expressions and equations | Lesson
• Creating expressions and equations | Worked example

Algebraic word problems | Lesson

• Algebraic word problems | Worked example
• Linear equations | Lesson
• Linear equations | Worked example
• Quadratic equations | Lesson
• Quadratic equations | Worked example

What are algebraic word problems?

What skills are needed.

• Translating sentences to equations
• Solving linear equations with one variable
• Evaluating algebraic expressions
• Solving problems using Venn diagrams

How do we solve algebraic word problems?

• Define a variable.
• Write an equation using the variable.
• Solve the equation.
• If the variable is not the answer to the word problem, use the variable to calculate the answer.

What's a Venn diagram?

• 7 + 10 − 13 = 4 ‍   brought both food and drinks.
• 7 − 4 = 3 ‍   brought only food.
• 10 − 4 = 6 ‍   brought only drinks.
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
• (Choice A)   $ 4 ‍   A $ 4 ‍  
• (Choice B)   $ 5 ‍   B $ 5 ‍  
• (Choice C)   $ 9 ‍   C $ 9 ‍  
• (Choice D)   $ 14 ‍   D $ 14 ‍  
• (Choice E)   $ 20 ‍   E $ 20 ‍  
• (Choice A)   10 ‍   A 10 ‍  
• (Choice B)   12 ‍   B 12 ‍  
• (Choice C)   24 ‍   C 24 ‍  
• (Choice D)   30 ‍   D 30 ‍  
• (Choice E)   32 ‍   E 32 ‍  
• (Choice A)   4 ‍   A 4 ‍  
• (Choice B)   10 ‍   B 10 ‍  
• (Choice C)   14 ‍   C 14 ‍  
• (Choice D)   18 ‍   D 18 ‍  
• (Choice E)   22 ‍   E 22 ‍  

Things to remember

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Word Problems Calculators: (41) lessons

2 number word problems.

Free 2 number Word Problems Calculator - This calculator handles word problems in the format below: * Two numbers have a sum of 70 and a product of 1189 What are the numbers? * Two numbers have a sum of 70. Their difference 32

2 Unknown Word Problems

Free 2 Unknown Word Problems Calculator - Solves a word problem based on two unknown variables

Age Difference

Free Age Difference Calculator - Determines the ages for an age difference word problem.

Age Word Problems

Free Age Word Problems Calculator - Determines age in age word problems

Angle of Elevation

Free Angle of Elevation Calculator - Solves angle of elevation word problems

Free Break Even Calculator - Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point

Coin Combinations

Free Coin Combinations Calculator - Given a selection of coins and an amount, this determines the least amount of coins needed to reach that total.

Coin Total Word Problems

Free Coin Total Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value with a certain amount more or less of one coin than another

Coin Word Problems

Free Coin Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value

Collinear Points that form Unique Lines

Free Collinear Points that form Unique Lines Calculator - Solves the word problem, how many lines can be formed from (n) points no 3 of which are collinear.

Compare Raises

Free Compare Raises Calculator - Given two people with a salary and annual raise amount, this determines how long it takes for the person with the lower salary to catch the person with the higher salary.

Consecutive Integer Word Problems

Free Consecutive Integer Word Problems Calculator - Calculates the word problem for what two consecutive integers, if summed up or multiplied together, equal a number entered.

Cost Revenue Profit

Free Cost Revenue Profit Calculator - Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit

Free Decay Calculator - Determines decay based on an initial mass and decay percentage and time.

Distance Catch Up

Free Distance Catch Up Calculator - Calculates the amount of time that it takes for a person traveling at one speed to catch a person traveling at another speed when one person leaves at a later time.

Distance Rate and Time

Free Distance Rate and Time Calculator - Solves for distance, rate, or time in the equation d=rt based on 2 of the 3 variables being known.

Find two numbers word problems

Free Find two numbers word problems Calculator - Given two numbers with a sum of s where one number is n greater than another, this calculator determines both numbers.

Inclusive Number Word Problems

Free Inclusive Number Word Problems Calculator - Given an integer A and an integer B, this calculates the following inclusive word problem questions: 1) The Average of all numbers inclusive from A to B 2) The Count of all numbers inclusive from A to B 3) The Sum of all numbers inclusive from A to B

Free Map Scale Calculator - Solves map scale problems based on unit measurements

Markup Markdown

Free Markup Markdown Calculator - Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.

Numbers Word Problems

Free Numbers Word Problems Calculator - Solves various basic math and algebra word problems with numbers

Free Overtime Calculator - Solves overtime wage problems

Percent Off Problem

Free Percent Off Problem Calculator - Given the 3 items of a percent word problem, Reduced Price, percent off, and full price, this solves for any one of the three given two of the items.

Percentage of the Pie Word Problem

Free Percentage of the Pie Word Problem Calculator - This takes two or three fractions of ownership in some good or object, and figures out what remaining fraction is left over.

Percentage Word Problems

Free Percentage Word Problems Calculator - Solves percentage word problems

Population Doubling Time

Free Population Doubling Time Calculator - Determines population growth based on a doubling time.

Population Growth

Free Population Growth Calculator - Determines population growth based on an exponential growth model.

Product of Consecutive Numbers

Free Product of Consecutive Numbers Calculator - Finds the product of (n) consecutive integers, even or odd as well. Examples include: product of 2 consecutive integers product of 2 consecutive numbers product of 2 consecutive even integers product of 2 consecutive odd integers product of 2 consecutive even numbers product of 2 consecutive odd numbers product of two consecutive integers product of two consecutive odd integers product of two consecutive even integers product of two consecutive numbers product of two consecutive odd numbers product of two consecutive even numbers product of 3 consecutive integers product of 3 consecutive numbers product of 3 consecutive even integers product of 3 consecutive odd integers product of 3 consecutive even numbers product of 3 consecutive odd numbers product of three consecutive integers product of three consecutive odd integers product of three consecutive even integers product of three consecutive numbers product of three consecutive odd numbers product of three consecutive even numbers product of 4 consecutive integers product of 4 consecutive numbers product of 4 consecutive even integers product of 4 consecutive odd integers product of 4 consecutive even numbers product of 4 consecutive odd numbers product of four consecutive integers product of four consecutive odd integers product of four consecutive even integers product of four consecutive numbers product of four consecutive odd numbers product of four consecutive even numbers product of 5 consecutive integers product of 5 consecutive numbers product of 5 consecutive even integers product of 5 consecutive odd integers product of 5 consecutive even numbers product of 5 consecutive odd numbers product of five consecutive integers product of five consecutive odd integers product of five consecutive even integers product of five consecutive numbers product of five consecutive odd numbers product of five consecutive even numbers

Ratio Word Problems

Free Ratio Word Problems Calculator - Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number.

Rebound Ratio

Free Rebound Ratio Calculator - Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage

Slope Word Problems

Free Slope Word Problems Calculator - Solves slope word problems

Solution Mixture

Free Solution Mixture Calculator - Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.

Split Fund Interest

Free Split Fund Interest Calculator - Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.

Sum of Consecutive Numbers

Free Sum of Consecutive Numbers Calculator - Finds the sum of (n) consecutive integers, even or odd as well. Examples include: sum of 2 consecutive integers sum of 2 consecutive numbers sum of 2 consecutive even integers sum of 2 consecutive odd integers sum of 2 consecutive even numbers sum of 2 consecutive odd numbers sum of two consecutive integers sum of two consecutive odd integers sum of two consecutive even integers sum of two consecutive numbers sum of two consecutive odd numbers sum of two consecutive even numbers sum of 3 consecutive integers sum of 3 consecutive numbers sum of 3 consecutive even integers sum of 3 consecutive odd integers sum of 3 consecutive even numbers sum of 3 consecutive odd numbers sum of three consecutive integers sum of three consecutive odd integers sum of three consecutive even integers sum of three consecutive numbers sum of three consecutive odd numbers sum of three consecutive even numbers sum of 4 consecutive integers sum of 4 consecutive numbers sum of 4 consecutive even integers sum of 4 consecutive odd integers sum of 4 consecutive even numbers sum of 4 consecutive odd numbers sum of four consecutive integers sum of four consecutive odd integers sum of four consecutive even integers sum of four consecutive numbers sum of four consecutive odd numbers sum of four consecutive even numbers sum of 5 consecutive integers sum of 5 consecutive numbers sum of 5 consecutive even integers sum of 5 consecutive odd integers sum of 5 consecutive even numbers sum of 5 consecutive odd numbers sum of five consecutive integers sum of five consecutive odd integers sum of five consecutive even integers sum of five consecutive numbers sum of five consecutive odd numbers sum of five consecutive even numbers

Sum of Five Consecutive Integers

Free Sum of Five Consecutive Integers Calculator - Finds five consecutive integers, if applicable, who have a sum equal to a number. Sum of 5 consecutive integers

Sum of Four Consecutive Integers

Free Sum of Four Consecutive Integers Calculator - Finds four consecutive integers, if applicable, who have a sum equal to a number. Sum of 4 consecutive integers

Sum of the First (n) Numbers

Free Sum of the First (n) Numbers Calculator - Determines the sum of the first (n) * Whole Numbers * Natural Numbers * Even Numbers * Odd Numbers * Square Numbers * Cube Numbers * Fourth Power Numbers

Sum of Three Consecutive Integers

Free Sum of Three Consecutive Integers Calculator - Finds three consecutive integers, if applicable, who have a sum equal to a number. Sum of 3 consecutive integers

Free Sun Shadow Calculator - This solves for various components and scenarios of the sun shadow problem

Unit Savings

Free Unit Savings Calculator - A discount and savings word problem using 2 people and full prices versus discount prices.

Work Word Problems

Free Work Word Problems Calculator - Given Person or Object A doing a job in (r) units of time and Person or Object B doing a job in (s) units of time, this calculates how long it would take if they combined to do the job.

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10 Best Strategies for Solving Math Word Problems

1. Understand the Problem by Paraphrasing

2. identify key information and variables, 3. translate words into mathematical symbols, 4. break down the problem into manageable parts, 5. draw diagrams or visual representations, 6. use estimation to predict answers, 7. apply logical reasoning for unknown variables, 8. leverage similar problems as templates, 9. check answers in the context of the problem, 10. reflect and learn from mistakes.

Have you ever observed the look of confusion on a student’s face when they encounter a math word problem ? It’s a common sight in classrooms worldwide, underscoring the need for effective strategies for solving math word problems . The main hurdle in solving math word problems is not just the math itself but understanding how to translate the words into mathematical equations that can be solved.

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Generic advice like “read the problem carefully” or “practice more” often falls short in addressing students’ specific difficulties with word problems. Students need targeted math word problem strategies that address the root of their struggles head-on. 

A Guide on Steps to Solving Word Problems: 10 Strategies 

One of the first steps in tackling a math word problem is to make sure your students understand what the problem is asking. Encourage them to paraphrase the problem in their own words. This means they rewrite the problem using simpler language or break it down into more digestible parts. Paraphrasing helps students grasp the concept and focus on the problem’s core elements without getting lost in the complex wording.

Original Problem: “If a farmer has 15 apples and gives away 8, how many does he have left?”

Paraphrased: “A farmer had some apples. He gave some away. Now, how many apples does he have?”

This paraphrasing helps students identify the main action (giving away apples) and what they need to find out (how many apples are left).

Play these subtraction word problem games in the classroom for free:

Students often get overwhelmed by the details in word problems. Teach them to identify key information and variables essential for solving the problem. This includes numbers , operations ( addition , subtraction , multiplication , division ), and what the question is asking them to find. Highlighting or underlining can be very effective here. This visual differentiation can help students focus on what’s important, ignoring irrelevant details.

• Encourage students to underline numbers and circle keywords that indicate operations (like ‘total’ for addition and ‘left’ for subtraction).
• Teach them to write down what they’re solving for, such as “Find: Total apples left.”

Problem: “A classroom has 24 students. If 6 more students joined the class, how many students are there in total?”

Key Information:

• Original number of students (24)
• Students joined (6)
• Looking for the total number of students

Here are some fun addition word problems that your students can play for free:

The transition from the language of word problems to the language of mathematics is a critical skill. Teach your students to convert words into mathematical symbols and equations. This step is about recognizing keywords and phrases corresponding to mathematical operations and expressions .

Common Translations:

• “Total,” “sum,” “combined” → Addition (+)
• “Difference,” “less than,” “remain” → Subtraction (−)
• “Times,” “product of” → Multiplication (×)
• “Divided by,” “quotient of” → Division (÷)
• “Equals” → Equals sign (=)

Problem: “If one book costs $5, how much would 4 books cost?”

Translation: The word “costs” indicates a multiplication operation because we find the total cost of multiple items. Therefore, the equation is 4 × 5 = $20

Complex math word problems can often overwhelm students. Incorporating math strategies for problem solving, such as teaching them to break down the problem into smaller, more manageable parts, is a powerful approach to overcome this challenge. This means looking at the problem step by step rather than simultaneously trying to solve it. Breaking it down helps students focus on one aspect of the problem at a time, making finding the solution more straightforward.

Problem: “John has twice as many apples as Sarah. If Sarah has 5 apples, how many apples do they have together?”

Steps to Break Down the Problem:

Find out how many apples John has: Since John has twice as many apples as Sarah, and Sarah has 5, John has 5 × 2 = 10

Calculate the total number of apples: Add Sarah’s apples to John’s to find the total,  5 + 10 = 15

By splitting the problem into two parts, students can solve it without getting confused by all the details at once.

Explore these fun multiplication word problem games:

Diagrams and visual representations can be incredibly helpful for students, especially when dealing with spatial or quantity relationships in word problems. Encourage students to draw simple sketches or diagrams to represent the problem visually. This can include drawing bars for comparison, shapes for geometry problems, or even a simple distribution to better understand division or multiplication problems .

Problem: “A garden is 3 times as long as it is wide. If the width is 4 meters, how long is the garden?”

Visual Representation: Draw a rectangle and label the width as 4 meters. Then, sketch the length to represent it as three times the width visually, helping students see that the length is 4 × 3 = 12

Estimation is a valuable skill in solving math word problems, as it allows students to predict the answer’s ballpark figure before solving it precisely. Teaching students to use estimation can help them check their answers for reasonableness and avoid common mistakes.

Problem: “If a book costs $4.95 and you buy 3 books, approximately how much will you spend?”

Estimation Strategy: Round $4.95 to the nearest dollar ($5) and multiply by the number of books (3), so 5 × 3 = 15. Hence, the estimated total cost is about $15.

Estimation helps students understand whether their final answer is plausible, providing a quick way to check their work against a rough calculation.

Check out these fun estimation and prediction word problem worksheets that can be of great help:

When students encounter problems with unknown variables, it’s crucial to introduce them to logical reasoning. This strategy involves using the information in the problem to deduce the value of unknown variables logically. One of the most effective strategies for solving math word problems is working backward from the desired outcome. This means starting with the result and thinking about the steps leading to that result, which can be particularly useful in algebraic problems.

Problem: “A number added to three times itself equals 32. What is the number?”

Working Backward:

Let the unknown number be x.

The equation based on the problem is  x + 3x = 32

Solve for x by simplifying the equation to 4x=32, then dividing by 4 to find x=8.

By working backward, students can more easily connect the dots between the unknown variable and the information provided.

Practicing problems of similar structure can help students recognize patterns and apply known strategies to new situations. Encourage them to leverage similar problems as templates, analyzing how a solved problem’s strategy can apply to a new one. Creating a personal “problem bank”—a collection of solved problems—can be a valuable reference tool, helping students see the commonalities between different problems and reinforcing the strategies that work.

Suppose students have solved a problem about dividing a set of items among a group of people. In that case, they can use that strategy when encountering a similar problem, even if it’s about dividing money or sharing work equally.

It’s essential for students to learn the habit of checking their answers within the context of the problem to ensure their solutions make sense. This step involves going back to the original problem statement after solving it to verify that the answer fits logically with the given information. Providing a checklist for this process can help students systematically review their answers.

Checklist for Reviewing Answers:

• Re-read the problem: Ensure the question was understood correctly.
• Compare with the original problem: Does the answer make sense given the scenario?
• Use estimation: Does the precise answer align with an earlier estimation?
• Substitute back: If applicable, plug the answer into the problem to see if it works.

Problem: “If you divide 24 apples among 4 children, how many apples does each child get?”

After solving, students should check that they understood the problem (dividing apples equally).

Their answer (6 apples per child) fits logically with the number of apples and children.

Their estimation aligns with the actual calculation.

Substituting back 4×6=24 confirms the answer is correct.

Teaching students to apply logical reasoning, leverage solved problems as templates, and check their answers in context equips them with a robust toolkit for tackling math word problems efficiently and effectively.

One of the most effective ways for students to improve their problem-solving skills is by reflecting on their errors, especially with math word problems. Using word problem worksheets is one of the most effective strategies for solving word problems, and practicing word problems as it fosters a more thoughtful and reflective approach to problem-solving

These worksheets can provide a variety of problems that challenge students in different ways, allowing them to encounter and work through common pitfalls in a controlled setting. After completing a worksheet, students can review their answers, identify any mistakes, and then reflect on them in their mistake journal. This practice reinforces mathematical concepts and improves their math problem solving strategies over time.

3 Additional Tips for Enhancing Word Problem-Solving Skills

Before we dive into the importance of reflecting on mistakes, here are a few impactful tips to enhance students’ word problem-solving skills further:

1. Utilize Online Word Problem Games

Incorporate online games that focus on math word problems into your teaching. These interactive platforms make learning fun and engaging, allowing students to practice in a dynamic environment. Games can offer instant feedback and adaptive challenges, catering to individual learning speeds and styles.

Here are some word problem games that you can use for free:

2. Practice Regularly with Diverse Problems

Consistent practice with a wide range of word problems helps students become familiar with different questions and mathematical concepts. This exposure is crucial for building confidence and proficiency.

Start Practicing Word Problems with these Printable Word Problem Worksheets:

3. Encourage Group Work

Solving word problems in groups allows students to share strategies and learn from each other. A collaborative approach is one of the best strategies for solving math word problems that can unveil multiple methods for tackling the same problem, enriching students’ problem-solving toolkit.

Conclusion 

Mastering math word problems is a journey of small steps. Encourage your students to practice regularly, stay curious, and learn from their mistakes. These strategies for solving math word problems are stepping stones to turning challenges into achievements. Keep it simple, and watch your students grow their confidence and skills, one problem at a time.

Frequently Asked Questions (FAQs)

How can i help my students stay motivated when solving math word problems.

Encourage small victories and use engaging tools like online games to make practice fun and rewarding.

What's the best way to teach beginners word problems?

Begin with simple problems that integrate everyday scenarios to make the connection between math and real-life clear and relatable.

How often should students practice math word problems?

Regular, daily practice with various problems helps build confidence and problem-solving skills over time.

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Word Problem Practice Questions with Answer Key

• Posted by Brian Stocker
• Date February 13, 2019
• Comments 11 comments

Problem Solving – Word Problems

Word problems are mathematical problems using everyday language and real-world situations.  Some information is given and one or more pieces or information (variables) are missing.  You must understand the given information, identify the mathematical operations necessary to solve the problem, and then carry out those operations to obtain the missing information or variables.

The Biggest Tip!

Tackling word problems is much easier if you have a systematic approach which we outline below.

Here is the biggest tip for word problems practice. Practice regularly and systematically. Sounds simple and easy right? Yes it is, and yes it really does work.   Word problems are a way of thinking and require you to translate a real world problem into mathematical terms.

Some math instructors go so far as to say that learning how to think mathematically is the main reason for teaching word problems. So what do we mean by Practice regularly and systematically? Studying word problems and math in general requires a logical and mathematical frame of mind. The only way that you can get this is by practicing regularly, which means everyday.

How to Solve Word Problems

Types of Word Problems

Most Common Word Problem Mistakes on a Test

It is critical that you practice word problems  everyday for the 5 days before the exam as a bare minimum.  If you practice and miss a day, you have lost the mathematical frame of mind and the benefit of your previous practice is pretty much gone. Anyone who has done any number of math tests will agree – you have to practice everyday.

See Also Algebra Word Problems

Effective problem-solving skills are essential in many areas of life, from academia to the workplace and beyond. Developing the ability to solve word problems requires practice and patience, as well as a strong understanding of basic mathematical concepts and operations.

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Word problem practice questions.

1. A box contains 7 black pencils and 28 blue ones. What is the ratio between the black and blue pens?

a. 1:4 b. 2:7 c. 1:8 d. 1:9

2. The manager of a weaving factory estimates that if 10 machines run at 100% efficiency for 8 hours, they will produce 1450 meters of cloth. Due to some tech¬nical problems, 4 machines run of 95% efficiency and the remaining 6 at 90% efficiency. How many meters of cloth can these machines will produce in 8 hours?

a. 1334 meters b. 1310 meters c. 1300 meters d. 1285 meters

3. In a local election at polling station A, 945 voters cast their vote out of 1270 registered voters. At poll¬ing station B, 860 cast their vote out of 1050 regis¬tered voters and at station C, 1210 cast their vote out of 1440 registered voters. What is the total turnout from all three polling stations?

a. 70% b. 74% c. 76% d. 80%

4. If Lynn can type a page in p minutes, what portion of the page can she do in 5 minutes?

a. p/5 b. p – 5 c. p + 5 d. 5/p

5. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both to paint a house?

a. 2 hours and 24 minutes b. 3 hours and 12 minutes c. 3 hours and 44 minutes d. 4 hours and 10 minutes

6. Employees of a discount appliance store receive an additional 20% off the lowest price on any item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?

a. $280.90 b. $287.00 c. $292.50 d. $306.00

7. The sale price of a car is $12,590, which is 20% off the original price. What is the original price?

a. $14,310.40 b. $14,990.90 c. $15,108.00 d. $15,737.50

8. Richard gives ‘s’ amount of salary to each of his ‘n’ employees weekly. If he has ‘x’ amount of money, how many days he can employ these ‘n’ employees.

a. sx/7n b. 7x/nx c. nx/7s d. 7x/ns

9. A distributor purchased 550 kilograms of potatoes for $165. He distributed these at a rate of $6.4 per 20 kilograms to 15 shops, $3.4 per 10 kilograms to 12 shops and the remainder at $1.8 per 5 kilo¬grams. If his total distribution cost is $10, what will his profit be?

a. $10.40 b. $8.60 c. $14.90 d. $23.40

10. How much pay does Mr. Johnson receive if he gives half of his pay to his family, $250 to his land¬lord, and has exactly 3/7 of his pay left over?

a. $3600 b. $3500 c. $2800 d. $175042

11. The cost of waterproofing canvas is .50 a square yard. What’s the total cost for waterproofing a canvas truck cover that is 15’ x 24’?

a. $18.00 b. $6.67 c. $180.00 d. $20.00

1. A The ratio between black and blue pens is 7 to 28 or 7:28. Bring to the lowest terms by dividing both sides by 7 gives 1:4.

2. A At 100% efficiency 1 machine produces 1450/10 = 145 m of cloth. At 95% efficiency, 4 machines produce 4 * 145 * 95/100 = 551 m of cloth. At 90% efficiency, 6 machines produce 6 * 145 * 90/100 = 783 m of cloth. Total cloth produced by all 10 machines = 551 + 783 = 1334 m Since the information provided and the question are based on 8 hours, we did not need to use time to reach the answer.

The turnout at polling station A is 945 out of 1270 registered voters. So, the percentage turnout at station A is:

(945/1270) × 100% = 74.41%

The turnout at polling station B is 860 out of 1050 registered voters. So, the percentage turnout at station B is:

(860/1050) × 100% = 81.90%

The turnout at polling station C is 1210 out of 1440 registered voters. So, the percentage turnout at station C is:

(1210/1440) × 100% = 84.03%

To find the total turnout from all three polling stations, we need to add up the total number of voters and the total number of registered voters from all three stations:

Total number of voters = 945 + 860 + 1210 = 3015

Total number of registered voters = 1270 + 1050 + 1440 = 3760

The overall percentage turnout is:

(3015/3760) × 100% = 80.12%

Therefore, the total turnout from all three polling stations is 80.12% — rounding to 80%.

4. D This is a simple direct proportion problem: If Lynn can type 1 page in p minutes, then she can type x pages in 5 minutes We do cross multiplication: x * p = 5 * 1 Then, x = 5/p

5. A This is an inverse ratio problem. 1/x = 1/a + 1/b where a is the time Sally can paint a house, b is the time John can paint a house, x is the time Sally and John can together paint a house. So, 1/x = 1/4 + 1/6 … We use the least common multiple in the denominator that is 24: 1/x = 6/24 + 4/24 1/x = 10/24 x = 24/10 x = 2.4 hours. In other words; 2 hours + 0.4 hours = 2 hours + 0.4•60 minutes = 2 hours 24 minutes

The original price of the dishwasher is $450. During a 15% off sale, the price of the dishwasher will be reduced by:

15% of $450 = 0.15 x $450 = $67.50

So the sale price of the dishwasher will be:

$450 – $67.50 = $382.50

As an employee, the person receives an additional 20% off the lowest price, which is $382.50. We can calculate the additional discount as:

20% of $382.50 = 0.20 x $382.50 = $76.50

So the final price that the employee will pay for the dishwasher is:

$382.50 – $76.50 = $306.00

Therefore, the employee will pay $306.00 for the dishwasher.

7. D Original price = x, 80/100 = 12590/X, 80X = 1259000, X = 15,737.50.

8. D We are given that each of the n employees earns s amount of salary weekly. This means that one employee earns s salary weekly. So; Richard has ‘ns’ amount of money to employ n employees for a week. We are asked to find the number of days n employees can be employed with x amount of money. We can do simple direct proportion: If Richard can employ n employees for 7 days with ‘ns’ amount of money, Richard can employ n employees for y days with x amount of money … y is the number of days we need to find. We can do cross multiplication: y = (x * 7)/(ns) y = 7x/ns

9. B The distribution is done at three different rates and in three different amounts: $6.4 per 20 kilograms to 15 shops … 20•15 = 300 kilograms distributed $3.4 per 10 kilograms to 12 shops … 10•12 = 120 kilograms distributed 550 – (300 + 120) = 550 – 420 = 130 kilograms left. This 50 amount is distributed in 5 kilogram portions. So, this means that there are 130/5 = 26 shops. $1.8 per 130 kilograms. We need to find the amount he earned overall these distributions. $6.4 per 20 kilograms : 6.4•15 = $96 for 300 kilograms $3.4 per 10 kilograms : 3.4 *12 = $40.8 for 120 kilograms $1.8 per 5 kilograms : 1.8 * 26 = $46.8 for 130 kilograms So, he earned 96 + 40.8 + 46.8 = $ 183.6 The total distribution cost is given as $10 The profit is found by: Money earned – money spent … It is important to remember that he bought 550 kilograms of potatoes for $165 at the beginning: Profit = 183.6 – 10 – 165 = $8.6

10. B We check the fractions taking place in the question. We see that there is a “half” (that is 1/2) and 3/7. So, we multiply the denominators of these fractions to decide how to name the total money. We say that Mr. Johnson has 14x at the beginning; he gives half of this, meaning 7x, to his family. $250 to his landlord. He has 3/7 of his money left. 3/7 of 14x is equal to: 14x * (3/7) = 6x So, Spent money is: 7x + 250 Unspent money is: 6×51 Total money is: 14x Write an equation: total money = spent money + unspent money 14x = 7x + 250 + 6x 14x – 7x – 6x = 250 x = 250 We are asked to find the total money that is 14x: 14x = 14 * 250 = $3500

11. D First calculate total square feet, which is 15 * 24 = 360 ft 2 . Next, convert this value to square yards, (1 yards 2 = 9 ft 2 ) which is 360/9 = 40 yards 2 . At $0.50 per square yard, the total cost is 40 * 0.50 = $20.

• Not reading the problem carefully and thoroughly, so that you either misunderstand or solve the problem incorrectly.
• Not identifying the important information in the problem, such as the quantities, units, and the operation to be performed.
• Not translating the information in the problem into mathematical language and equations.
• Not checking the units of measure and making sure they match your final answer.
• Not double-checking the answer to ensure it makes sense.
• Not understanding the underlying mathematical concept or operation the problem is asking for.
• Not using estimation or approximations as a tool to check the reasonableness of your answer.

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11 Comments

Will we need to know units and their conversions such as yards to feet? Should we memorise those?

are we allowed to use a calculator? To expect someone to complete these in their head is absurd especially with a time limit. The second question requires multiplication by decimals, which would be okay if you got a whole number but you dont, you get a fraction and the only way to get it to 551 is by then multiplying that number by 4. Doubt anyone would be required to do these kind of calculations in a real world scenario especially unaided and under time constraints.

Hi Depends on the test – what test are you studying for?

is this preparation for the CAAT level C???

These questions vary in subject and difficulty level to give students practice on different types of questions for different types of tests. They are not specific to one test or one level.

Yes the LEAST common multiple of 6 and 4 is 12 – i did it with 24 – it will give the same answer no matter which way you do it. Good point though – perhaps for simplicity sake 12 would be better.

Are these questions appeared on the Cbest?

The are the same TYPE of questions – not exactly

sorry for the message above, i like your site and i have won 1st place in an exam due to this site

I used Chat GPT. Solved every one…. perfectly. I’m still dumb as a rock though.

Oh Really? You may want to check that again!! It gave me wrong answers and weird steps to calculate for 2 of them!

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Word problems are one of the first ways we see applied math, and also one of the most anxiety producing math challenges many grade school kids face. This page has a great collection of word problems that provide a gentle introduction to word problems for all four basic math operations. You'll find addition word problems, subtraction word problems, multiplication word problems and division word problems, all starting with simple easy-to-solve questions that build up to more complex skills necessary for many standardized tests. As they progress, you'll also find a mix of operations that require students to figure out which type of story problem they need to solve. And if you need help, check out word problem tricks at the bottom of this page!

Addition Word Problems

20 word problems worksheets.

These introductory word problems for addition are perfect for first grade or second grade applied math.

Subtraction Word Problems

These worksheets include simple word problems for subtraction with smaller quantities. Watch for words like difference and remaining.

Mixed Addition and Subtraction Word Problems

8 word problems worksheets.

This set of worksheets includes a mix of addition and subtraction word problems. Students are required to figured out which operation to apply given the problem context.

Multiplication Word Problems

This is the first set of word problem worksheets the introduces multiplication. These worksheets include only multiplication story problems; see worksheets in the following sections for mixed operations.

Division Word Problems

These division story problems deal with only whole divisions (quotients without remainders.) This is a great first step to recognizing the keywords that signal you are solving a division word problem.

Girl Scout Cookie Division

If you've been working as Troop Cookie Mom (or Dad!) you'll know what kind of math we've been practicing... These worksheets are primarily division word problems that introduce remainders. Pull your tagalongs or your thin mints out of the box and figure out how many remainders you'll be allowed to eat!

Division With Remainders Word Problems

24 word problems worksheets.

The worksheets in this section are made up of story problems using division and involving remainders. These are similar to the Girl Scout problems in the prior section, but with different units.

Mixed Multiplication and Division Word Problems

This worksheets combine basic multiplication and division word problems. The division problems do not include remainders. These worksheets require the students to differentiate between the phrasing of a story problem that requires multiplication versus one that requires division to reach the answer.

Mixed Operation Word Problems

The whole enchilada! These workshes mix addition, subtraction, multiplication and division word problems. These worksheets will test a students ability to choose the correct operation based on the story problem text.

Extra Facts Addition Word Problems

One way to make a word problem slightly more complex is to include extra (but unused) information in the problem text. These worksheets have addition word problems with extra unused facts in the problem.

Extra Facts Subtraction Word Problems

Word problem worksheets for subtraction with extra unused facts in each problem. The worksheets start out with subtraction problems with smaller values and progress through more difficult problems.

Extra Facts Addition and Subtraction Word Problems

Mixed operation addition and subtraction word problem worksheets with extra unused facts in the problems.

Extra Facts Multiplication Word Problems

Word problems for multiplication with extra unused facts in the problem. The worksheets in this set start out with multiplication problems with smaller values and progress through more difficult problems.

Extra Facts Division Word Problems

The worksheets in this section include math word problems for division with extra unused facts in the problem. The quotients in these division problems do not include remainders.

Extra Facts Multiplication and Division Word Problems

16 word problems worksheets.

This is a collection of worksheets with mixed multiplication and division word problems and extra unused facts in the problem. The quotients in these division problems do not include remainders.

Travel Time Word Problems (Customary)

28 word problems worksheets.

These story problems deal with travel time, including determining the travel distance, travel time and speed using miles (customary units). This is a very common class of word problem and specific practice with these worksheets will prepare students when they encounter similar problems on standardized tests.

Travel Time Word Problems (Metric)

Wondering when the train arrives? These story problems deal with travel time, including determining the travel distance, travel time and speed using kilometers (metric units).

Tricks for Solving Word Problems

The math worksheets on this section of the site deal with simple word problems appropriate for primary grades. The simple addition word problems can be introduced very early, in first or second grade depending on student aptitude. Follow those worksheets up with the subtraction word problems once subtraction concept are covered, and then proceed with multiplication and division word problems in the same fashion.

Word problems are often a source of anxiety for students because we tend to introduce math operations in the abstract. Students struggle to apply even elementary operations to word problems unless they have been taught consistently to think about math operations in their day to day routines. Talking with kids regularly about 'how many more do you need' or 'how many do you have left over' or other seemingly simple questions when asked regularly can build that basic number sense that helps enormously when word problems and applied math start to show up.

There are many tricks for solving word problems that can bridge the gap, and they can be helpful tools if students are either struggling with where to start with a problem or just need a way to check their thinking on a particular problem.

Make sure your student reads the entire problem first. It is very easy to start reading a word problem and think after the first sentence or two that 'I know what they're asking for...' and then have the problem take an entirely different turn. Overcoming this early solution bias can be difficult, and it is much better to develop the habit of making a complete pass over the problem before deciding on a path to the solution.

There are particular words that seem to show up in word problems for different operations that can tip you off to what might be the correct operation to apply. These key words aren't a sure-fire way to know what to do with a problem, but they can be a useful starting point.

For example, phrases like 'combined,' 'total,' 'together' or 'sum' are very often signals that the problem is going to involve addition.

Subtraction word problems very often use words such as 'difference,' 'less,' or 'decrease' in their wording. Word problems for younger kids will also use verbs like 'gave' or 'shared' as a stand-in for subtraction.

The key phrases to watch out for multiplication word problems include obvious ones like 'times' and 'product,' but also be on the look out for 'for each' and 'every.'

Learning when to apply division in a word problem can be tricky, especially for younger kids who haven't fully developed a concept of what division can be used for... But that's exactly why division word problems can be so useful! If you see words like 'per' or 'among' in the word problem text, your division radar should be sounding off loud and clear. Pay attention to 'shared among' and make sure students don't confuse this phrasing with a subtraction word problem. That's a clear example of when paying attention to the language is very important.

Number Line

The Algebra Calculator is a versatile online tool designed to simplify algebraic problem-solving for users of all levels. Here's how to make the most of it:

• Begin by typing your algebraic expression into the above input field, or scanning the problem with your camera.
• After entering the equation, click the 'Go' button to generate instant solutions.
• The calculator provides detailed step-by-step solutions, aiding in understanding the underlying concepts.
• -x+3\gt 2x+1
• (x+5)(x-5)\gt 0
• 10^{1-x}=10^4
• \sqrt{3+x}=-2
• 6+11x+6x^2+x^3=0
• factor\:x^{2}-5x+6
• simplify\:\frac{2}{3}-\frac{3}{2}+\frac{1}{4}
• x+2y=2x-5,\:x-y=3

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• High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,...

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Word problems (or story problems) allow kids to apply what they've learned in math class to real-world situations.  Word problems build higher-order thinking, critical problem-solving, and reasoning skills.

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Mixed word problems (stories) for skills working on subtraction,addition, fractions and more.

A full index of all math worksheets on this site.

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> Word Problems calculators AtoZmath.com - Homework help (with all solution steps) Secondary school, High school and College Provide step by step solutions of your problems using online calculators (online solvers) Your textbook, etc Word Problems Calculators ( ) Word Problems with example Here first term a = 1, d = 4 - 1 = 3 We know that, f(n) = a + (n - 1)d f(10) = 1 + (10 - 1)(3) = 1 + (27) = 28 We know that, S_n = / [2a + (n - 1)d] ∴ S_10 = 10/2 [2(1) + (10 - 1)(3)] = 5 [2 + (27)] = 5 [29] = 145 Hence, 10th Term Of The Given Series is 28 And Sum of First 10th Term is 145 For arithemetic progression addition of 3 terms is 27 and their multiplication is 648, then that nos. Find the sum of all natural nos between 100 to 200 and which are not divisible by 4. For arithemetic progression, addition of three terms is 51 and multiplication of end terms is 273, then find that nos. For arithemetic progression, addition of 4 terms is 4 and addition of multiplication of end terms and multiplication of middle terms is -38, then find that nos. Here a = 3, r = 6 / 3 = 2 We know that, a_n = a * r^(n-1) a_10 = 3 * (2)^(10 - 1) = 3 * (512) = 1536 We know that, S_n = a (r^n - 1)/(r - 1) ∴ S_10 = 3 * ((2)^10 - 1) / (2 - 1) => S_10 = 3 * (1024 - 1) / 1 => S_10 = 3 * 1023 / 1 => S_10 = 3069 Hence, 10th term of the given series is 1536 and sum of first 10th term is 3069 For geometric progression addition of 3 terms is 26 and their multiplication is 216, then that nos. For geometric progression multiplication of 5 terms is 1 and 5th term is 81 times then the 1st term. Arithmetic mean of two no is 13 and geometric mean is 12, then find that nos. Find 6 geometric mean between 1 and 256. Find 1 + 2 + 3 + ... + 10 Find 1 + 2 + 3 + ... 10 terms Here P = Rs. 730 , R = 25/4 % and Time = 184 days = 184 / 365 years S.I. = P*R*N/100 = ( 730 * 25/4 * 184 /365) / 100 = 23 Simple Interest is Rs. 23 . The interest on a certain amount of money at 8% per year for a period of 4 years is Rs 512. Find the sum of money. A sum of money lent at simple interest amounts to Rs 1596 in 3/2 years and to 1860 in 5/2 years. Find the sum & the rate of interest. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 3 % highere rate, it whould have fetched Rs. 300 more. Find the sum. A shopkeeper borrowed Rs. 20000 from two money lenders. For one loan he paid 12% and for the other 14% per annum. After one year, he paid Rs. 2560 as interest. How much did he borrow at each rate ? At what rate percent per annum will sum of money double in 8 years? Rajeev deposited money in the post office which is doubled in 20 years at a simple rate of interest. In how many years will the original sum triple itself? Here P = Rs. 4500 , R = 10 %, N = 3 yrs. A = P (1 + R/100)^N = 4500 * ( 1 + 10 / 100 ) ^ 3 = 4500 * ( 110 / 100 ) ^ 3 = 5989.5 Therefore, C.I. = Rs. ( 5989.5 - 4500 ) = Rs. 1489.5 . What sum of money becomes Rs. 9261 in 3 years at 5% per annum, compounded annually ? A sum of money amounts to Rs 6690 after 3 years and to Rs 10035 after 6 years on compound interest. Calculate the sum of money. The difference between the compound interest and the simple interest on a certain sum at 10 % per annum for 2 years is Rs. 52 . Find the sum. If the compound interest on a certain sum for 3 years at 10 % per annum be Rs. 331, what would be the simple interest ? A sum of money 2 times itself at compound interest in 15 years. In how many years, it will become 8 times of itself ? Other no = ( HCF * LCM ) / Given No = ( 14 * 11592 ) / 504 = 322 . Find the largest no which can exactly divide 513 , 783 , 1107 Find the smallest no exactly divisible by 12 , 15 , 20 and 27 . Find the least no which when divided by 6 , 7 , 8 , 9 , 12 leaves the same remainder 2 in each case. Find the largest no which divides 77 , 147 , 252 to leave the same remainder in each case. The greatest no that will divide 290 , 460 , 552 leaving respectively 4 , 5 , 6 as remainder. LCM of two nos is 14 times their HCF. The sum of LCM and HCF is 600 . If one no is 280 , then find the other no ? Cash Price = 440 Down Payemnt = 200 Remaining Balance = 440 - 200 = 240 The installment to be paid at the end of 1 months = 244 Therefore the interest charged on Rs 240, for a period of 1 months = Rs 244 - Rs 240 = 4 If R % is the rate of interest per annum, then (240 × R × 1) / (100 × 12) = 4 R = 20 Thus, the rate of interest charged under the installment plan is = 20 per annum A washing machine is available at Rs 6400 cash or for Rs 1400 cash down payment and 5 monthly installments of Rs 1030 each. Calculate the rate of interest charged under the instalment plan. A computer is sold by a company for Rs 19200 cash or for Rs 4800 cash down payment together with 5 equal monthly installments. If the rate of interest charged by the company is 12% per annum, find each installment. A man borrows money from a finance company and has to pay it back in 2 equal half yearly installments of Rs 4945 each. If the interest is charged by the finance company at the rate of 15 % per annum compounded as installment plan, find the principal and the total interest paid. Ram borrowed a sum of money and returned it in 3 equal quarterly installments of Rs 17576 each. Find the sum borrowed, if the rate of interest charged was 16 % per annum compounded as installment plan. Find also the total interest charged. 20 % of 80 = ( 20 / 100 × 80 ) = 16 . A's annual income is increased from Rs 60000 to Rs 75000 . Find the percentage of increase in A's income. In a school of 225 boys, 15 were absent then what percent were present ? A earns 25 % more than B. By what percent does B earn less then A. A reduction of 20 % in the price of basmati rice would enable a man to buy 2 kg of rice more for Rs 250. Find the reduced price per kg. Find the selling price of an item, of which the printed price is Rs 25000 if the successive discounts given are 10 %, 8 % and 4 %. The successive discount of 10 % and 5 % are given on the purchased Computer. If the final price of the Computer is Rs 10260, then find the printed price of the Computer. C.P. = Rs. 50 , Gain = 10 % S.P. = C.P. × / = 50 × / = 55 Rs. C.P. = Rs. 50 , Loss = 10 % S.P. = C.P. × / = 50 × / = 45 Rs. Find cost price when selling price = 55 , Loss/Gain = 10 % Find Loss/Gain % when cost price = 50 and selling price = 55 By selling an article for Rs 110 a man loses 12 %. For how much should he sell it to gain 8 %. A man sells two houses for Rs 536850 each. On one he gains and on the other he loses 5 %. Find his gain or loss % on the whole transaction. If selling price of 10 articles is the same as the cost price of 12 articles, find the gain %. If the marked price of an article is Rs. 380 and a discount of 5 % is given on it, what is the selling price ? A cycle dealer marks his goods 25 % above his cost price and allows a discount of 8 % on it. Find his gain percent. Successive discounts of 20 % and 10 % equivalent to a single discount of how many percent? Here Mean = 12.5 and n=10 `Sigma`(X) = × n = 12.5 × 10 = 125 `:.` the correct sum `Sigma`(X) = 125 - (Wrong Observation) + (Correct Observation) = 125 - (-8) + (8) = 141 . `:.` correct mean = / = / = 14.1 Here `Sigma`(X) = 343 and n= 15 If we remove two observation then 13 observation left. Sum of 13 observation `Sigma`(X') = 343 - ( ( 18 ) + ( 26 ) ) = 299 Then the mean of remaining 13 observations = / = / = 23. 120 Math Word Problems To Challenge Students Grades 1 to 8 Written by Marcus Guido Hey teachers! 👋 Use Prodigy to spark a love for math in your students – including when solving word problems! Teaching Tools Subtraction Multiplication Mixed operations Ordering and number sense Comparing and sequencing Physical measurement Ratios and percentages Probability and data relationships You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems. A jolt of creativity would help. But it doesn’t come. Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge. This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes. There are 120 examples in total. The list of examples is supplemented by tips to create engaging and challenging math word problems. 120 Math word problems, categorized by skill Addition word problems. Best for: 1st grade, 2nd grade 1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total? 2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now? 3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now? 4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total? 5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies? 6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June? 7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now? 8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total? Subtraction word problems Best for: 1st grade, second grade 9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left? 10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing? 11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now? Practice math word problems with Prodigy Math Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade! 12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half? 13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now? 14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month? 15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left? 16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left? Multiplication word problems Best for: 2nd grade, 3rd grade 17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have? 18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total? 19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year? 20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total? 21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn? Division word problems Best for: 3rd grade, 4th grade, 5th grade 22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag? 23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on? 24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total? 25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost? 26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible? Mixed operations word problems 27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now? 28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order? 29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have? 30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag? Ordering and number sense word problems 31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total? 32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total? 33. Composing Numbers: What number is 6 tens and 10 ones? 34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I? 35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points? Fractions word problems Best for: 3rd grade, 4th grade, 5th grade, 6th grade 36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar? 37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait? 38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total? 39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink? 40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total? 41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left? 42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete? 43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use? 44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction. 45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make? 46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number. Decimals word problems Best for: 4th grade, 5th grade 47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total? 48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left? 49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked? 50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower? 51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo? 52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week? Comparing and sequencing word problems Best for: Kindergarten, 1st grade, 2nd grade 53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more? 54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more? 55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs? 56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers? 57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20? 58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36? 59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April? Time word problems 66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her? 69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school? 70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for? 71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home? Money word problems Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade 60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total? 61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left? 62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times? 63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost? 64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total? 65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left? 67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional. 68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year? Physical measurement word problems Best for: 1st grade, 2nd grade, 3rd grade, 4th grade 72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler? 73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres? 74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years? 75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year? 76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink? 77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get? 78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy? 79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total? 80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres? 81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction? Ratios and percentages word problems Best for: 4th grade, 5th grade, 6th grade 82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have? 83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers? 84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players? 85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport? 86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population? 87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there? 88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average? Probability and data relationships word problems Best for: 4th grade, 5th grade, 6th grade, 7th grade 89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased? 90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1? 91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction. 92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni? 93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test? 94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal? 95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y . Geometry word problems Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade 96. Introducing Perimeter:  The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter? 97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total? 98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume? 99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw? 100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter? 101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area? 102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw? 103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm? 104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy? 105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle? 106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it? 107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it? 108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it? 109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides? 110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units? 111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side? 112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter? 113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield? 114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius? Variables word problems Best for: 6th grade, 7th grade, 8th grade 115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent? 116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored. 117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast. 118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored. 119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive. 120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours? How to easily make your own math word problems & word problems worksheets Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do: Link to Student Interests:  By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback. Make Questions Topical:  Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge. Include Student Names:  Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem. Be Explicit:  Repeating keywords distills the question, helping students focus on the core problem. Test Reading Comprehension:  Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary. Focus on Similar Interests:  Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students. Feature Red Herrings:  Including unnecessary information introduces another problem-solving element, overwhelming many elementary students. A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones. Final thoughts about math word problems You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students. Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments. The result? A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach. 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A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem. For instance, does this sound familiar? Johnny has 12 apples. If he gives four to Susie, how many will he have left? You could solve this problem by looking at the numbers and figuring out what the problem is asking you to do. In this case, you're supposed to find out how many apples Johnny has left at the end of the problem. By reading the problem, you know Johnny starts out with 12 apples. By the end, he has 4 less because he gave them away. You could write this as: 12 - 4 = 8 , so you know Johnny has 8 apples left. Word problems in algebra If you were able to solve this problem, you should also be able to solve algebra word problems. Yes, they involve more complicated math, but they use the same basic problem-solving skills as simpler word problems. You can tackle any word problem by following these five steps: Read through the problem carefully, and figure out what it's about. Represent unknown numbers with variables. Translate the rest of the problem into a mathematical expression. Solve the problem. Check your work. We'll work through an algebra word problem using these steps. Here's a typical problem: The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took two days, and the van cost $360. How many miles did she drive? It might seem complicated at first glance, but we already have all of the information we need to solve it. Let's go through it step by step. Step 1: Read through the problem carefully. With any problem, start by reading through the problem. As you're reading, consider: What question is the problem asking? What information do you already have? Let's take a look at our problem again. What question is the problem asking? In other words, what are you trying to find out? The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost $360. How many miles did she drive? There's only one question here. We're trying to find out how many miles Jada drove . Now we need to locate any information that will help us answer this question. There are a few important things we know that will help us figure out the total mileage Jada drove: The van cost $30 per day. In addition to paying a daily charge, Jada paid $0.50 per mile. Jada had the van for 2 days. The total cost was $360 . Step 2: Represent unknown numbers with variables. In algebra, you represent unknown numbers with letters called variables . (To learn more about variables, see our lesson on reading algebraic expressions .) You can use a variable in the place of any amount you don't know. Looking at our problem, do you see a quantity we should represent with a variable? It's often the number we're trying to find out. Since we're trying to find the total number of miles Jada drove, we'll represent that amount with a variable—at least until we know it. We'll use the variable m for miles . Of course, we could use any variable, but m should be easy to remember. Step 3: Translate the rest of the problem. Let's take another look at the problem, with the facts we'll use to solve it highlighted. The rate to rent a small moving van is $30 per day , plus $0.50 per mile . Jada rented a van to drive to her new home. It took 2 days , and the van cost $360 . How many miles did she drive? We know the total cost of the van, and we know that it includes a fee for the number of days, plus another fee for the number of miles. It's $30 per day, and $0.50 per mile. A simpler way to say this would be: $30 per day plus $0.50 per mile is $360. If you look at this sentence and the original problem, you can see that they basically say the same thing: It cost Jada $30 per day and $0.50 per mile, and her total cost was $360 . The shorter version will be easier to translate into a mathematical expression. Let's start by translating $30 per day . To calculate the cost of something that costs a certain amount per day, you'd multiply the per-day cost by the number of days—in other words, 30 per day could be written as 30 ⋅ days, or 30 times the number of days . (Not sure why you'd translate it this way? Check out our lesson on writing algebraic expressions .) $30 per day and $.50 per mile is $360 $30 ⋅ day + $.50 ⋅ mile = $360 As you can see, there were a few other words we could translate into operators, so and $.50 became + $.50 , $.50 per mile became $.50 ⋅ mile , and is became = . Next, we'll add in the numbers and variables we already know. We already know the number of days Jada drove, 2 , so we can replace that. We've also already said we'll use m to represent the number of miles, so we can replace that too. We should also take the dollar signs off of the money amounts to make them consistent with the other numbers. 30 ⋅ 2 + .5 ⋅ m = 360 Now we have our expression. All that's left to do is solve it. Step 4: Solve the problem. This problem will take a few steps to solve. (If you're not sure how to do the math in this section, you might want to review our lesson on simplifying expressions .) First, let's simplify the expression as much as possible. We can multiply 30 and 2, so let's go ahead and do that. We can also write .5 ⋅ m as 0.5 m . 60 + .5m = 360 Next, we need to do what we can to get the m alone on the left side of the equals sign. Once we do that, we'll know what m is equal to—in other words, it will let us know the number of miles in our word problem. We can start by getting rid of the 60 on the left side by subtracting it from both sides . 60 + .5m = 360 -60 -60 The only thing left to get rid of is .5 . Since it's being multiplied with m , we'll do the reverse and divide both sides of the equation with it. .5m = 300 .5 .5 .5 m / .5 is m and 300 / 0.50 is 600 , so m = 600 . In other words, the answer to our problem is 600 —we now know Jada drove 600 miles. Step 5: Check the problem. To make sure we solved the problem correctly, we should check our work. To do this, we can use the answer we just got— 600 —and calculate backward to find another of the quantities in our problem. In other words, if our answer for Jada's distance is correct, we should be able to use it to work backward and find another value, like the total cost. Let's take another look at the problem. According to the problem, the van costs $30 per day and $0.50 per mile. If Jada really did drive 600 miles in 2 days, she could calculate the cost like this: $30 per day and $0.50 per mile 30 ⋅ day + .5 ⋅ mile 30 ⋅ 2 + .5 ⋅ 600 According to our math, the van would cost $360, which is exactly what the problem says. This means our solution was correct. We're done! While some word problems will be more complicated than others, you can use these basic steps to approach any word problem. On the next page, you can try it for yourself. Let's practice with a couple more problems. You can solve these problems the same way we solved the first one—just follow the problem-solving steps we covered earlier. For your reference, these steps are: If you get stuck, you might want to review the problem on page 1. You can also take a look at our lesson on writing algebraic expressions for some tips on translating written words into math. Try completing this problem on your own. When you're done, move on to the next page to check your answer and see an explanation of the steps. A single ticket to the fair costs $8. A family pass costs $25 more than half of that. How much does a family pass cost? Here's another problem to do on your own. As with the last problem, you can find the answer and explanation to this one on the next page. Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo. Between the two of them, they donated $280. How much money did Mo give? Problem 1 Answer Here's Problem 1: A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost? Answer: $29 Let's solve this problem step by step. We'll solve it the same way we solved the problem on page 1. Step 1: Read through the problem carefully The first in solving any word problem is to find out what question the problem is asking you to solve and identify the information that will help you solve it . Let's look at the problem again. The question is right there in plain sight: So is the information we'll need to answer the question: A single ticket costs $8 . The family pass costs $25 more than half the price of the single ticket. Step 2: Represent the unknown numbers with variables The unknown number in this problem is the cost of the family pass . We'll represent it with the variable f . Step 3: Translate the rest of the problem Let's look at the problem again. This time, the important facts are highlighted. A single ticket to the fair costs $8 . A family pass costs $25 more than half that . How much does a family pass cost? In other words, we could say that the cost of a family pass equals half of $8, plus $25 . To turn this into a problem we can solve, we'll have to translate it into math. Here's how: First, replace the cost of a family pass with our variable f . f equals half of $8 plus $25 Next, take out the dollar signs and replace words like plus and equals with operators. f = half of 8 + 25 Finally, translate the rest of the problem. Half of can be written as 1/2 times , or 1/2 ⋅ : f = 1/2 ⋅ 8 + 25 Step 4: Solve the problem Now all we have to do is solve our problem. Like with any problem, we can solve this one by following the order of operations. f is already alone on the left side of the equation, so all we have to do is calculate the right side. First, multiply 1/2 by 8 . 1/2 ⋅ 8 is 4 . Next, add 4 and 25. 4 + 25 equals 29 . That's it! f is equal to 29. In other words, the cost of a family pass is $29 . Step 5: Check your work Finally, let's check our work by working backward from our answer. In this case, we should be able to correctly calculate the cost of a single ticket by using the cost we calculated for the family pass. Let's look at the original problem again. We calculated that a family pass costs $29. Our problem says the pass costs $25 more than half the cost of a single ticket. In other words, half the cost of a single ticket will be $25 less than $29. We could translate this into this equation, with s standing for the cost of a single ticket. 1/2s = 29 - 25 Let's work on the right side first. 29 - 25 is 4 . To find the value of s , we have to get it alone on the left side of the equation. This means getting rid of 1/2 . To do this, we'll multiply each side by the inverse of 1/2: 2 . According to our math, s = 8 . In other words, if the family pass costs $29, the single ticket will cost $8. Looking at our original problem, that's correct! So now we're sure about the answer to our problem: The cost of a family pass is $29 . Problem 2 Answer Here's Problem 2: Answer: $70 Let's go through this problem one step at a time. Start by asking what question the problem is asking you to solve and identifying the information that will help you solve it . What's the question here? To solve the problem, you'll have to find out how much money Mo gave to charity. All the important information you need is in the problem: The amount Flor donated is three times as much the amount Mo donated Flor and Mo's donations add up to $280 total The unknown number we're trying to identify in this problem is Mo's donation . We'll represent it with the variable m . Here's the problem again. This time, the important facts are highlighted. Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo . Between the two of them, they donated $280 . How much money did Mo give? The important facts of the problem could also be expressed this way: Mo's donation plus Flor's donation equals $280 Because we know that Flor's donation is three times as much as Mo's donation, we could go even further and say: Mo's donation plus three times Mo's donation equals $280 We can translate this into a math problem in only a few steps. Here's how: Because we've already said we'll represent the amount of Mo's donation with the variable m , let's start by replacing Mo's donation with m . m plus three times m equals $280 Next, we can put in mathematical operators in place of certain words. We'll also take out the dollar sign. m + three times m = 280 Finally, let's write three times mathematically. Three times m can also be written as 3 ⋅ m , or just 3 m . m + 3m = 280 It will only take a few steps to solve this problem. To get the correct answer, we'll have to get m alone on one side of the equation. To start, let's add m and 3 m . That's 4 m . We can get rid of the 4 next to the m by dividing both sides by 4. 4 m / 4 is m , and 280 / 4 is 70 . We've got our answer: m = 70 . In other words, Mo donated $70 . The answer to our problem is $70 , but we should check just to be sure. Let's look at our problem again. If our answer is correct, $70 and three times $70 should add up to $280 . We can write our new equation like this: 70 + 3 ⋅ 70 = 280 The order of operations calls for us to multiply first. 3 ⋅ 70 is 210. 70 + 210 = 280 The last step is to add 70 and 210. 70 plus 210 equals 280 . 280 is the combined cost of the tickets in our original problem. Our answer is correct : Mo gave $70 to charity. /en/algebra-topics/distance-word-problems/content/ 185 IMAGES K5 Provides Answers to Math Word Problems Worksheets Elapsed Time Word Problems Using Equations To Solve Word Problems Worksheets Answer Key Grades K-5 Activity: Solving Word Problems Algebra Word Problems Worksheet With Solutions Rational Equation Word Problems With Answers VIDEO Solve Word Problems 3rd Grade How to solve Word Problems How to Solve EASY Math Word Problems HOW TO SOLVE WORD PROBLEM IN SAT MATHS Solve Math Word Problem with Ease 📖 Step by step answers explained for Math Questions for kids 📖 Sets COMMENTS Word Problems Calculator Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer. How do you identify word problems in math? Word problems in math can be identified by the use of language that describes a situation or scenario. Math Problem Solver Problem Solver Subjects. 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