Algebra 1 Worksheets
Word Problems Worksheets
Here is a graphic preview for all of the Word Problems Worksheets. You can select different variables to customize these Word Problems Worksheets for your needs. The Word Problems Worksheets are randomly created and will never repeat so you have an endless supply of quality Word Problems Worksheets to use in the classroom or at home. Our Word Problems Worksheets are free to download, easy to use, and very flexible.
These Word Problems Worksheets are a good resource for students in the 5th Grade, 6th Grade, 7th Grade, and 8th Grade.
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Distance, Rate,
of Operations
Description of Word Problems Worksheets
One Step Equation Word Problems These Algebra 1 Equations Worksheets will produce one step word problems. These worksheets will produce ten problems per worksheet. These Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.
Two Step Equation Word Problems These Algebra 1 Equations Worksheets will produce two step word problems. These worksheets will produce ten problems per worksheet. These Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.
Distance, Rate, and Time Word Problems These Algebra 1 Equations Worksheets will produce distance, rate, and time word problems with ten problems per worksheet. You may select the numbers to be represented with digits or in words. These Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.
Mixture Word Problems These Algebra 1 Equations Worksheets will produce mixtures word problems with ten problems per worksheet. You may select the numbers to be represented with digits or in words. These Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.
Work Word Problems These Algebra 1 Equations Worksheets will produce work word problems with ten problems per worksheet. You may select the numbers to be represented with digits or in words. These Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.
Algebraic Expressions Worksheets
Algebraic expression worksheet helps students to understand algebra. This topic is the key to solving several broad-ranging topics. Number theory, geometry, and other analysis use algebraic expressions to unlock the answers to various problems. Most equations in mathematics see the use of algebra.
Benefits of Algebraic Expressions Worksheets
By practicing several questions related to the topic, a student will be sure to master the subject. An algebraic expression worksheet constitutes applying various arithmetic operations, word problems, and geometric interpretations, etc.
One of the most important benefits of these math worksheets is that they help solve problems faster and more accurately. For students, solving problems with a gradual increase in the level of difficulty of the questions proves to be very advantageous. It gives them a better understanding of the topic at hand.
Download Algebraic Expressions Worksheet PDFs
Algebraic expressions worksheets are used to help students grasp various concepts related to algebra and other sister topics. It also helps students to sharpen their calculation skills.
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Writing Algebraic Expressions: Worksheets with Answers
Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.
Mathster keyboard_arrow_up Back to Top
Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers.
| Worksheet Name | 1 | 2 | 3 |
|---|---|---|---|
| Construct Expressions, Formula and Equations – Basics | |||
| Construct Expressions, Formula and Equations |
Corbett Maths keyboard_arrow_up Back to Top
Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. It really is one of the very best websites around.
| Name | Questions | Solutions |
|---|---|---|
| Algebra: expressions – forming | ||
| Algebra: notation |
Algebraic Sentences Problems
Algebraic sentences word problems.
An algebraic sentence when written in equation form involves algebraic expressions (which contain variables such as letters in the alphabet), constants, and an equal symbol. Each algebraic sentence may contain a combination of algebraic expressions and constants, or with just two or more algebraic expressions. Almost always, the word “is” in an algebraic sentence denotes the symbol of equality.
In our example above, the algebraic sentence, “ Five more than twice a number is forty-three “, is translated and written into its equation form: [latex]2x + 5 = 43[/latex].
But before we delve into solving word problems that involve algebraic sentences, it’s crucial that we become familiar with how to translate and write algebraic expressions.
Algebraic Expressions
Learning how to write and translate algebraic expressions is the foundation in writing algebraic sentences. Eventually, we will use this knowledge to write algebraic equations where we solve for the value of the unknown variable.
What is an algebraic expression?
Think of an algebraic expression as the equivalent of a phrase in the English language. It does not convey a complete thought but is an important building block in constructing a sentence. Algebraic expressions consist of numbers, variables, and arithmetic operations.
Let’s take a quick look at some math phrases that were translated and written into algebraic expressions.
- the sum of a number and [latex]8[/latex] [latex]\large{\,\,\, \to \,\,\,\, {\color{red}{c + 8}}}[/latex]
- [latex]3[/latex] less than a number [latex]\large{\,\,\, \to \,\,\,\, {\color{red}{y – 3}}}[/latex]
- the product of [latex]45[/latex] and [latex]m[/latex] [latex]\large{\,\,\, \to \,\,\,\,{\color{red}{45m}}}[/latex]
- a number divided by [latex]2[/latex] [latex]\large{\,\,\, \to \,\,\,\,\Large {\color{red}{x \over 2}}}[/latex]
Translating and Writing Algebraic Sentences
Once you know how to translate math phrases into algebraic expressions, it’ll be easy for you to translate and write algebraic sentences in an equation form as well.
For instance, how do you write “ the difference of 16 and k is seven ” into an algebraic equation?
Let’s deconstruct this algebraic sentence.
You may notice that we translated “the difference of [latex]16[/latex] and [latex]k[/latex]” into an algebraic expression, [latex]16-k[/latex], then used the equal symbol ([latex]=[/latex]) in place of the word “is”.
As I mentioned at the beginning of this lesson, the word “is” in an algebraic sentence, most of the time, signifies the equality symbol which is the case in this example.
Therefore, we can write this algebraic sentence in equation form as [latex]16 – k = 7[/latex].
Now that we are confident in translating algebraic sentences and writing them in an equation format, it’s time for us to take one step further. We will not only translate and write algebraic sentences into algebraic equations but also proceed to solve them.
Examples of Algebraic Sentences Word Problems
The main key when solving word problems with algebraic sentences is to accurately translate the algebraic expressions then set up and write each algebraic equation correctly. In doing so, we can ensure that we are solving the right equation and as a result, will get the correct answer for each word problem.
Example 1: Six more than seven times a number is thirty-four. Find the number.
First, let’s deconstruct the algebraic sentence. It’s important that we identify and separate the algebraic expressions from the constants as well as determine if the problem suggests equality between the terms.
For the unknown value, we’ll use [latex]\large{x}[/latex] as our variable.
Note: Since addition is commutative, changing the order of the addends on the left side of the equation does not change the sum. Therefore, we may also write the algebraic expression as [latex]7x+6[/latex] or the algebraic equation as [latex]7x + 6 = 34[/latex] instead.
However, for our discussion, we will use [latex]6 + 7x = 34[/latex] as our equation.
The original problem asks us to find the number which in this case is [latex]\large{x}[/latex]. So our next step is to solve for [latex]\large{x}[/latex] in our equation, [latex]6 + 7x = 34[/latex].
Now, we’ll evaluate the value of [latex]\large{x = 4}[/latex] to verify if the number we found satisfies the original algebraic sentence.
Remember that we are asked to find the identity of “the number” in our algebraic sentence and NOT the value of the variable [latex]\large{x}[/latex]. Therefore, it will be incorrect to say that [latex]\large{x=4}[/latex] is the answer. This is a common mistake that we always need to pay attention to.
We’ll replace the variable [latex]\large{x}[/latex] with the number [latex]4[/latex] to see if the algebraic expression on the left side of the equation also results to [latex]34[/latex].
Yes, it does! This means that number 4 is the answer .
Example 2: The difference between three times a number and five is sixteen. Find the number.
Right away, the word “difference” in our algebraic sentence gives us a clue that we will be using the subtraction operation. But, unlike, in addition, the order of the terms within an expression matters in subtraction. So we have to make sure that the terms in our algebraic expression are set up in the correct order.
Another keyword is “times”, which suggests that [latex]3[/latex] is being multiplied to a number whose value is currently unknown.
This time, let’s use [latex]\large{g}[/latex] as our variable. Start by translating the algebraic expression correctly then continue to write the equation.
Now that we have our equation, let’s find out what the unknown value is by solving for the variable, [latex]\large{g}[/latex].
As discussed in our first example, it is important that we verify if the result of our solution makes the algebraic equation true. For this one, I will leave it up to you to evaluate the value of [latex]\large{g = 7}[/latex]. Remember to replace the unknown value of the variable [latex]\large{g}[/latex] with the number [latex]7[/latex] to see if the left side of the equation is also equal to [latex]16[/latex].
Since the original algebraic sentence requires us to find the number, then the answer is number 7 .
Example 3: A number decreased by half of the number is four. Find the number.
This algebraic sentence is quite interesting because we don’t just have one unknown value, but two! First, we have the “number” (the unknown) then the “half of the number”, which means one-half of the unknown.
The keyword “half of” also indicates multiplying something by one-half while the “decreased by” tells us that we will be subtracting one term from the other.
To organize our thoughts, let’s deconstruct this algebraic sentence into its meat and potatoes.
Being able to break apart our algebraic sentence into its basic parts allows us to read the sentence thoroughly and understand the relationship between its quantities.
After setting up our algebraic equation, our next step is to solve it for [latex]\large{m}[/latex].
We need to evaluate the value of [latex]\large{m = 8}[/latex] to check if the number we got makes our algebraic equation true.
Great! The values on both sides of the equation are equal to each other. Therefore, the number 8 is the correct answer to our original algebraic sentence.
Example 4: Four times the sum of twice a number and six is thirty-two. Find the number.
Looking closely, we see a few keywords that would help us in translating this algebraic sentence into an equation.
- times – means that we’ll be multiplying [latex]4[/latex] by the quantity, “sum of twice a number and six”
- sum – means that we need to add the terms, “ twice a number ” and six
- twice – means that a number (the unknown value) is multiplied by [latex]2[/latex]
With these in mind, let’s write our algebraic equation.
Notice that we used the variable [latex]\large{d}[/latex] in our equation to stand for our unknown value. Let’s now proceed and solve for [latex]\large{d}[/latex] and afterward, check if the value we get indeed makes the equation true.
Evaluate the value of [latex]\large{d = 1}[/latex]:
Looks like everything checks out, so the answer to our algebraic sentence is the number 1 .
Example 5: Two-thirds of the sum of three times a number and six is ten. What is the number?
This problem involves a fraction and an algebraic expression as you can tell. The keyword “of” indicates multiplication, so it tells us that we need to multiply the fraction [latex]\large{2 \over 3}[/latex] by the sum of the two given quantities (“three times a number” and six).
Let’s move on and write our algebraic equation. We’ll use the variable [latex]\large{y}[/latex] as the placeholder for our “number” whose value is currently unknown.
Awesome! We are able to translate our algebraic sentence into an equation. It’s time for us to solve for [latex]\large{y}[/latex] then I’ll leave it up to you to do a check if the number we find as the value of [latex]\large{y}[/latex] makes the algebraic equation true.
Once you evaluate [latex]\large{y = 3}[/latex], you’ll see that the answer to our word problem is indeed the number 3 .
Example 6: Twice the difference of a number and three is four more than the number. Find the number.
We have an example here that is a little different from the word problems we’ve covered so far. In this algebraic sentence, both sides of the equation contain an algebraic expression. However, the keywords present will help us translate it correctly into an equation so there’s nothing to worry about.
- twice – means that we will multiply the quantity (difference of a number and three) by [latex]2[/latex]
- difference – tells us to use the subtraction operation between our unknown value (“number”) and three
- more than – means that we need to add four to our unknown value
Let’s solve for our unknown value, [latex]\large{a}[/latex], then verify that our result makes the algebraic equation true.
Evaluate the value of [latex]\large{a = 10}[/latex]:
Perfect! The value we got for [latex]\large{a}[/latex] which is [latex]10[/latex], made our equation equal on both sides. Thus, the answer is the number 10 .
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Algebraic Expressions Worked Examples
Linear Equation Word Problems Worksheet
Students will practice solving linear equation word problems.
Example Questions
Other Details
This is a 4 part worksheet:
- Part I Model Problems
- Part II Practice
- Part III Challenge Problems
- Part IV Answer Key
- Interactive Slope : explore the formula of slope by clicking and dragging two points.
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Grade 9 Algebra Word Problems
Related Pages Grade 8 Algebra Word Problems Algebra Word Problems Solving Equations More Algebra Lessons
These lessons cover grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step-by-step solutions. It includes various examples and solutions for algebra word problems that you will commonly encounter in 9th grade.
| Algebra Word Problems | ||
|---|---|---|
Age Word Problems
Age Problems with two unknowns or variables
Example: Taylor is five times as old as Spenser. The sum of their ages is eighteen. How old are Taylor and Spencer?
Solution: Let x represent Spenser’s age Therefore, Taylor’s age is 5x x + 5x = 18 6x = 18 x = 3 Therefore, Spenser is 3 years old and Taylor is 15 years old.
Grade 9 Algebra Word Problems - Age
Example 1: A mother is three times as old as her daughter. Six years ago, the mother’s age was six tines that of her daughter. How old are they now?
Solution: Let x represent the daughter’s age. Therefore, 3x is the mother’s age. 6(x - 6) = 3x - 6 6x - 6 = 3x - 6 3x = 30 x = 10 Therefore, the daughter’s is 10 years old and the mother is 30 years old.
Example 2: A father is now three times as old as his son. Eight years ago, the father was five times as old as his son. How old are they now?
Rate, Distance, Time Word Problems
Grade 9 Algebra Word Problems - Rate, Distance, Time
Example: A bus leaves the terminal and averages 40 km/hr. One hour late, a second bus leaves the same terminal and averages 50 km/hr. In how many hours will the second bus overtake the first?
Grade 9 Rate, Distance, Time Word Problems
Example 1: One motorist travels 5 km.hr faster than another. They leave from the same place and travel in opposite directions. What is the rate of each if they are 195 km apart after 3 hours?
Example 2: A pilot flew from airport A to airport B at a rate of 100 km/hr and flew back from airport B to airport A at 120 km/hr. The total time it took was 11 hours. How far is it from airport A to airport B?
Coin Word Problems
Grade 9 Algebra Word Problems - Coins
Example: A coin collection amounting to $25 consists of nickels and dimes. There are 3 times as many nickels and dimes. There are 3 times as many nickels as dimes. How many coins of each kind are there?
Solution: Let x = number of dimes 3x = number of nickels 10x + 5(3x) = 2500 25x = 2500 x = 100 Therefore, there are 100 dimes and 300 nickels.
Grade 9 Coin Algebra Word Problems
Example: Mr. Rogers has $4.62. He has 3 times as many dimes as nickels and 6 more pennies than dimes. How many coins of each kind does he have?
Coin Algebra Word Problems - Grade 9
Example: Bob has in his pocket a number of pennies, 5 times as many nickels as pennies and 5 more quarters than pennies. The coins amount to $2.27. Find the number of each kind of coin.
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Praxis Core Math
Course: praxis core math > unit 1.
- Algebraic properties | Lesson
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- Equivalent expressions | Lesson
- Equivalent expressions | Worked example
- Creating expressions and equations | Lesson
- Creating expressions and equations | Worked example
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Algebraic word problems | Worked example
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Video transcript
IMAGES
VIDEO
COMMENTS
Basic Algebra Word Problems 1) Write each expression and solve. ("find the number") a) The sum of 14 and a number is 41. b) 8 plus the product of 21 and a number is 71 c) The difference between 104 and a number is 79 d) five minus the product of two and a number is 12 e) Twelve is one-eighth of a number 2) Answer carefrlly.
WordProbPacket2. Algebra Word Problems Packet #1. On a separate sheet of paper, write your "Let" statement(s) to define the unknown. Solve each problem using an algebraic equation. 1. Twice a number is 500 more than six times the number. What is the number? 2.
Objective a: Reading and translating word problems 3 There are a couple of special words that you also need to remember. Double or twice a number means 2x, and triple or thrice a number means 3x. Example 1: Use the tables above to translate the following English phrases into algebraic expressions. Let x the unknown number. A) 5 more than a number.
Examples, solutions, videos, worksheets, games and activities to help Algebra 1 or grade 7 students learn how to write algebraic expressions from word problems. Beginning Algebra & Word Problem Steps. Name what x is. Define everything in the problem in terms of x. Write the equation.
Work Word Problems. 3) It takes Trevon ten hours to clean an attic. Cody can clean the same attic in seven hours. Find how long it would take them if they worked together. 5) Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours. Had he done it alone it would have taken Daniel.
Examples, solutions, videos, and worksheets to help Grade 7 students review how to solve word problems using Algebra. How to solve word problems using Algebra? Algebra word problems require translating real-world scenarios into algebraic expressions and equations to find solutions. Here are some common types of algebra word problems:
Translating verbal descriptions into algebraic expressions is an essential initial step in solving word problems. Benefits of Algebra Word Problems Worksheets. We use algebra in our everyday life without even realising it. Solving algebraic word problems worksheets help kids relate and understand the relevance of algebra in the real world.
Distance, Rate, and Time Word Problems. These Algebra 1 Equations Worksheets will produce distance, rate, and time word problems with ten problems per worksheet. You may select the numbers to be represented with digits or in words. These Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.
members. Write an expression to determine the number of invitations she will have each committee member write. b. If Grace has 220 invitations for the committee members to write, how many will she have each member write? Write an algebraic expression and use it to evaluate each word problem. 8. Arturo purchased a package of 50 blank CDs.
Algebraic Expressions Worksheets. Algebraic expression worksheet helps students to understand algebra. This topic is the key to solving several broad-ranging topics. Number theory, geometry, and other analysis use algebraic expressions to unlock the answers to various problems. Most equations in mathematics see the use of algebra.
Printable. (Answers on the second page.) Write Expressions for Word Problems Worksheet #1. Write Expressions for Word Problems Worksheet #2. Online or Generated. Evaluate Expressions by Substitution. Simplify Expressions by Write Expressions for Word Problems. Simplify Expressions using Distributive Property. Use Distributive Property & Combine ...
Answer: 34,62 4. When the sum of a number and 3 is subtracted from 10 the result is 5. Identify the integer. Solution: The sum of a number and 3 is: x+3 Write the problem as a mathematical sentence, meaning convert each phrase into the corresponding part of the equation: 10 - (x+3) = 5 Now solve with algebra:
Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers. Worksheet Name. 1. 2. 3. Construct Expressions, Formula and Equations - Basics. 1. 2.
Objective: Students will identify like terms. Students will simplify algebraic expressions by combining like terms. Quantities that you ADD to form an algebraic expression are called terms. 4n + 6b - 8. You CAN add/subtract like terms. You CANNOT add/subtract unlike terms. For each algebraic expression, identify the number of terms. Then list ...
Solving algebraic word problems requires us to combine our ability to create equations and solve them. To solve an algebraic word problem: 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.
es. more than the first.4. The sum of the interior angles of a triangle is 180 ̊, The second angle of a triangle is 45 ̊ more than the first and the third a. gl. is twice the first.5. The area of a triangle is half th. b. se times the height.6. The perimeter of a rectangle is the sum of twice the len. th.
Almost always, the word "is" in an algebraic sentence denotes the symbol of equality. In our example above, the algebraic sentence, "Five more than twice a number is forty-three", is translated and written into its equation form: [latex]2x + 5 = 43[/latex]. But before we delve into solving word problems that involve algebraic sentences ...
Enjoy these free printable sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key. Algebra. Distance Formula. Equation of Circle. Factoring. Factor Trinomials Worksheet. Functions and Relations.
Show Video Lesson. Grade 8 number word problems - common core. How to write word problems into systems of linear equations and solve systems of linear equations using elimination and substitution methods? Example 1: The sum of two numbers is 361 and the difference between the two numbers is 173.
Free worksheet(pdf) and answer key on the solving word problems based on linear equations and real world linear models. Scaffolded questions that start relatively easy and end with some real challenges. ... Example Questions. Other Details. This is a 4 part worksheet: Part I Model Problems; Part II Practice; Part III Challenge Problems; Part IV ...
The table below lists some key words and phrases that are used to describe common mathematical operations. To write. algebraic expressions and equations, assign a variable to represent the unknown number. In the table below, the letter. "x" is used to represent the unknown. In translation problems, the words. sum, total, difference, product ...
Grade 8 Algebra Word Problems Algebra Word Problems Solving Equations More Algebra Lessons. These lessons cover grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step-by-step solutions. It includes various examples and solutions for algebra word problems that you will commonly encounter in 9th grade.
4 years ago. At the end of a snow storm, Elijah saw there was a lot of snow on his front lawn. The temperature increased and the snow began to melt at a steady rate. There was a depth of 18 inches of snow on the lawn when the storm ended and then it started melting at a rate of 1.5 inches per hour. Write an equation for S,S, in terms of t,t ...