fraction problem solving questions grade 5

Fraction Word Problems (Grade 5)

These lessons, with videos, examples and solutions help Grade 5 students learn to solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Related Pages Common Core for Grade 5 More Lessons for Grade 5

For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Common Core: 5.NF.2

Suggested Learning Targets

• I can solve addition and subtraction word problems with fractions.
• I can estimate fractions to make sense of my answer.

Solve Fraction Word Problems with Visual Bar Models

Example: Kayla weighed her Halloween treats. She counted 1/4 of a pound of lollipops and 2/7 of a pound of gobstoppers. She also counted 1/3 of a pound of mints. How many pounds of candy did Kayla have altogether?

Add mixed numbers word problems

Example: While gardening, Jan spend 1 3/4 hours planting and 2 1/8 hours trimming. What was the total hours worked by Jan in her garden?

Solve word problems involving addition of fractions - unlike denominators

Example: Matthew ran 1/6 of a mile then took a break before running another 3/4 of a mile. How far did Matthew run in all?

Subtracting Fractions From Whole Numbers Solve a word problem using bar models.

Example: A craft store has a 9-yard spool of ribbon. In the morning, a customer buys 1/5 yard of ribbon from the spool. In the afternoon, another customer buys 7/10 yard of ribbon from the spool. How much ribbon is left?

Adding and subtracting unlike fractions word problems

• Drew and Maddy were filling the class raised garden bed with soil. Drew shoveled in 1/3 of a cubic yard, and Maddy shoveled in 1/2 of a cubic yard. How much soil did they put into the garden bed altogether?
• Caden invited Owen over to his house. Caden shared his chocolate stash from last Halloween. He still had 4/5 of a pound of chocolate. Caden asked Owen how much chocolate he would like. Owen said that he would like 1/3 of a pound of chocolate. How much chocolate does Caden have left?

Adding and subtracting mixed numbers word problems

• Jaida went gold panning and found 1 1/5 pounds of gold. The next day she found 3 1/4 pound more. How much total gold did Jaida find?
• Jonathan collected 4 1/2 kilograms of filberts. He gave 2 3/4 kilograms to his friend. How many kilograms of filberts does Jonathan have now?

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5th Grade Fractions Worksheets

5th grade fractions worksheets are a simple way to implement the learning of fractions and their types. A fraction is some part of a whole object. The ratio of these two quantities is called a fraction. Part of the fraction placed at the top is the numerator, and the other is called the denominator. There are many types of fractions: proper, improper, mixed, like, unlike, and equal. Working with fractions necessitates a sound conceptual understanding through constant practice.

Benefits of Grade 5 Fractions Worksheets

5th grade fractions worksheets are a highly reliable means of acquiring an in-depth knowledge of fractions and their types. These 5th grade math worksheets are thoughtfully curated to impart a thorough understanding of all fraction concepts. Such well-curated worksheets are reliable means of enhancing a child’s ability to visualize the fractions in everyday lives. By practicing multiple problems covered in these worksheets, a child can quickly grasp both easy and complicated concepts quickly.

☛ Practice : Grade 5 Interactive Fractions Worksheets

Printable PDFs Fractions Worksheets for Grade 5

For better understanding and more practice, download the free version of the 5th grade fraction worksheets. It is available in a pdf format and can be used easily anywhere.

• Math 5th Grade Fractions Worksheet
• Grade 5 Math Fractions Worksheet
• 5th Grade Math Fractions Worksheet
• Fractions Worksheet for 5th Grade

Interactive 5th Grade Fractions Worksheets

• A Recap to Fractions Worksheet for 4th Grade
• Grade 4 Comparing Fractions Worksheet
• Ordering Fractions Worksheet for Grade 4

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Fraction word prob.

Fraction word problems

Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.

Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.

What are fraction word problems?

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.

To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.

After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.

For example,

Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?

You can follow these steps to solve the problem:

Step-by-step guide: Adding and subtracting fractions

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Multiplying and dividing fractions

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4 th grade math to 6 th grade math?

• Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
• Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
• Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
• Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
• Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?

[FREE] Fraction Operations Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

How to solve fraction word problems

In order to solve fraction word problems:

Determine what operation is needed to solve.

Write an equation.

Solve the equation.

State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators).

Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?

The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.

2 Write an equation.

3 Solve the equation.

To add fractions with like denominators, add the numerators and keep the denominators the same.

4 State your answer in a sentence.

The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.

Julia and her brother ate \cfrac{5}{8} of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?

The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.

To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.

\cfrac{5}{6}+\cfrac{1}{3}= \, ?

The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.

That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.

\cfrac{1 \times 2}{3 \times 2}=\cfrac{2}{6}

Now you can add the fractions and simplify the answer.

\cfrac{5}{6}+\cfrac{2}{6}=\cfrac{7}{6}=1 \cfrac{1}{6}

Tim ran a total of 1 \cfrac{1}{6} miles.

Example 3: subtracting fractions (like denominators)

Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?

The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.

To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.

\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}

Pia walked \cfrac{1}{7} of a mile farther to the park than back home.

Example 4: subtracting fractions (unlike denominators)

Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?

The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.

To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.

\cfrac{7}{8}-\cfrac{1}{3}= \, ?

The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.

That means both fractions will need to be changed so that their denominator is 24.

To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.

\begin{aligned}&\cfrac{7 \times 3}{8 \times 3}=\cfrac{21}{24} \\\\ &\cfrac{1 \times 8}{3 \times 8}=\cfrac{8}{24} \end{aligned}

Now you can subtract the fractions.

\cfrac{21}{24}-\cfrac{8}{24}=\cfrac{13}{24}

Henry has \cfrac{13}{24} of a pound of beef left.

Example 5: multiplying fractions

Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?

It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.

However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.

The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.

To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”

\cfrac{1}{2} \times \cfrac{3}{4}= \, ?

To multiply fractions, multiply the numerators and multiply the denominators.

\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}

Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.

Example 6: dividing fractions

Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?

The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.

To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.

To divide fractions, multiply the dividend by the reciprocal of the divisor.

\begin{aligned}& \cfrac{7}{8} \div \cfrac{1}{4}= \, ? \\\\ & \downarrow \downarrow \downarrow \\\\ &\cfrac{7}{8} \times \cfrac{4}{1}=\cfrac{28}{8} \end{aligned}

You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.

Nia can make 3 \cfrac{1}{2} cup servings.

Teaching tips for fraction word problems

• Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
• Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
• Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
• As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
• Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
• There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.

Easy mistakes to make

• Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
• Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
• Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.

Related fractions operations lessons

• Fractions operations
• Multiplicative inverse
• Reciprocal math
• Fractions as divisions

Practice fraction word problem questions

1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?

Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.

Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.

Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.

Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.

To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.

\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.

Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”

2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?

The area of the garden is 1\cfrac{23}{36} square meters.

The area of the garden is \cfrac{27}{32} square meters.

The area of the garden is \cfrac{2}{3} square meters.

The perimeter of the garden is \cfrac{2}{3} meters.

To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.

\cfrac{24}{36} can be simplified to \cfrac{2}{3}. 

Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”

3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?

Zoe ate \cfrac{3}{64} more of the cake than Liam.

Zoe ate \cfrac{1}{4} more of the cake than Liam.

Zoe ate \cfrac{1}{8} more of the cake than Liam.

Liam ate \cfrac{1}{4} more of the cake than Zoe.

To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.

\cfrac{2}{8} can be simplified to \cfrac{1}{4}. 

Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”

4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?

Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.

Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.

Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.

Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.

To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}.  Then you can add.

\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}. 

Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”

5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?

Killian used \cfrac{2}{10} gallons of paint in all.

Killian used \cfrac{1}{5} gallons of paint in all.

Killian used \cfrac{63}{100} gallons of paint in all.

Killian used 1 \cfrac{3}{5} gallons of paint in all.

To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.

\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.

Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”

6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.

He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?

Evan filled \cfrac{2}{25} cups.

Evan filled 8 cups.

Evan filled \cfrac{9}{10} cups.

Evan filled 7 cups.

To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

\cfrac{40}{5} can be simplifed to 8.

Therefore, the correct answer is “Evan filled 8 cups.”

Fraction word problems FAQs

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.

To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.

Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.

The next lessons are

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Word Problems on Fraction

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

1.  4/7 of a number is 84. Find the number. Solution: According to the problem, 4/7 of a number = 84 Number = 84 × 7/4 [Here we need to multiply 84 by the reciprocal of 4/7]

= 21 × 7 = 147 Therefore, the number is 147.

2.  Rachel took \(\frac{1}{2}\) hour to paint a table and \(\frac{1}{3}\) hour to paint a chair. How much time did she take in all?

3. If 3\(\frac{1}{2}\) m of wire is cut from a piece of 10 m long wire, how much of wire is left?

Total length of the wire = 10 m

Fraction of the wire cut out = 3\(\frac{1}{2}\) m = \(\frac{7}{2}\) m

Length of the wire left = 10 m – 3\(\frac{1}{2}\) m

            = [\(\frac{10}{1}\) - \(\frac{7}{2}\)] m,    [L.C.M. of 1, 2 is 2]

            = [\(\frac{20}{2}\) - \(\frac{7}{2}\)] m,    [\(\frac{10}{1}\) × \(\frac{2}{2}\)]

            = [\(\frac{20 - 7}{2}\)] m

            = \(\frac{13}{2}\) m

            = 6\(\frac{1}{2}\) m

4. One half of the students in a school are girls, 3/5 of these girls are studying in lower classes. What fraction of girls are studying in lower classes?

Fraction of girls studying in school = 1/2

Fraction of girls studying in lower classes = 3/5 of 1/2

                                                            = 3/5 × 1/2

                                                            = (3 × 1)/(5 × 2)

                                                            = 3/10

Therefore, 3/10 of girls studying in lower classes.

5.  Maddy reads three-fifth of 75 pages of his lesson. How many more pages he need to complete the lesson? Solution: Maddy reads = 3/5 of 75 = 3/5 × 75

= 45 pages. Maddy has to read = 75 – 45. = 30 pages. Therefore, Maddy has to read 30 more pages. 6.  A herd of cows gives 4 litres of milk each day. But each cow gives one-third of total milk each day. They give 24 litres milk in six days. How many cows are there in the herd? Solution: A herd of cows gives 4 litres of milk each day. Each cow gives one-third of total milk each day = 1/3 of 4 Therefore, each cow gives 4/3 of milk each day. Total no. of cows = 4 ÷ 4/3                          = 4 × ¾                          = 3 Therefore there are 3 cows in the herd.

Questions and Answers on Word problems on Fractions:

1. Shelly walked \(\frac{1}{3}\) km. Kelly walked \(\frac{4}{15}\) km. Who walked farther? How much farther did one walk than the other?

2. A frog took three jumps. The first jump was \(\frac{2}{3}\) m long, the second was \(\frac{5}{6}\) m long and the third was \(\frac{1}{3}\) m long. How far did the frog jump in all?

3. A vessel contains 1\(\frac{1}{2}\) l of milk. John drinks \(\frac{1}{4}\) l of milk; Joe drinks \(\frac{1}{2}\) l of milk. How much of milk is left in the vessel?

●   Multiplication is Repeated Addition.

●  Multiplication of Fractional Number by a Whole Number.

●  Multiplication of a Fraction by Fraction.

●  Properties of Multiplication of Fractional Numbers.

●  Multiplicative Inverse.

●  Worksheet on Multiplication on Fraction.

●  Division of a Fraction by a Whole Number.

●  Division of a Fractional Number.

●  Division of a Whole Number by a Fraction.

●  Properties of Fractional Division.

●  Worksheet on Division of Fractions.

●  Simplification of Fractions.

●  Worksheet on Simplification of Fractions.

●  Word Problems on Fraction.

●  Worksheet on Word Problems on Fractions.

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• What is fraction? A fraction is a numerical quantity that is not a whole number. For example, ½ is a fraction of 1 as numerator and 2 as a denominator

Fractions having the same denominator are called like fractions. For example, ½,3/2, 5/2, 7/2, are all like fractions.

• Fractions having different denominators are called, unlike fractions. For example, ½, 2/3, ¾, 4/5, are all unlike fractions
• A fraction whose numerator is less than the denominator is called proper fraction. For example, 8/9, 7/8, 6/7, 5/6 are all proper fractions.
• A fraction whose numerator is greater than the denominator is called improper fraction. For example, 3/2, 4/3, 5/4, 6/5 are all improper fractions.

EXAMPLE 1: Find the fraction of shaded and unshaded part.

EXAMPLE 2: Find the fraction of red balls, green balls and blue balls.

SOLUTION: Total number of balls= 10 Number of red balls= 4

Fraction of red balls= 4/10= 2/5

Fraction of green balls= 5/10= ½

Fraction of blue balls= 1/10

Fraction as a division

• Any fraction can be expressed as a division by writing its numerator as dividend and denominator as divisor

Numerator/Denominator

= Dividend ÷ Divisor

=Dividend/Divisor

EXAMPLE 1: Write 1÷2 as a fraction.

SOLUTION: ½

EXAMPLE 2: Write 2/3 as division.

SOLUTION: 2÷3

To convert a mixed no. into an improper fraction & vice versa

• To convert a mixed number into an improper fraction multiply the quotient with the divisor and add the product with remainder in the numerator. The denominator will contain the divisor.

• To convert an improper fraction into a mixed number, divide the numerator of the fraction by the denominator. Write the quotient as the whole number. The remainder in the numerator and the divisor in the denominator.

Finding and checking equivalent fraction

• To find the equivalent fraction to a given fraction, divide or multiply the numerator or denominator by the same number. (other than zero)

• To check for equivalent fractions, we need two equivalent fraction.

SOLUTION: 2x4=8 3X3=9 8≠9

Hence, the fractions are not equal.

To find a fraction in its lowest term

• A fraction is in its lowest term when the numerator and the denominator don’t have a common factor, except 1.
• There are two methods of finding a fraction in its lowest term. They are: Method 1: Divide the numerator and denominator with their common factor till we are left with only the common factor 1

Method 2: Divide the numerator and denominator of the given fraction with their HCF.

To find the fraction of a number or quantity

• Divide the number by the denominator. Then, multiply the quotient so obtained by the numerator.

EXAMPLE 1: A group has 120 children. 4/5 of them are girls. Find the number of boys.

No. of boys= (120-96) = 24

EXAMPLE 2: Find 1/4 of a year in months.

SOLUTION: A year has 12 months. ¼ X 12 = 3 months [ANS]

To compare unlike fractions

• First find the LCM of the denominators of the given fractions.
• Then convert the unlike fractions into equivalent like fraction with LCM as their common denominator.
• Compare the like fractions.

Convert mixed fractions into improper fractions to compare them.

To add/subtract unlike fractions

• Find the LCM of the denominator of unlike fraction.
• Then convert the unlike fraction into equivalent like fraction with LCM as common denominator.
• Add/subtract the like fraction so obtained.

EXAMPLE 1: Add/subtract ½ and/from 1/6.

SOLUTION: LCM of 2 and 6 is = 2x3=6 2| 2,6 1,3

Reciprocal of a fractional number

• When the product of two fraction is 1, we say that each of the fraction is the reciprocal or multiplicative inverse of the other.

Division of fractions

• Division is repeated subtraction.
• Division by a fraction is same as multiplication by its reciprocal. 0 has no reciprocal. The reciprocal of 1 is 1. 0 divided by any non-zero number = 0

Practice these questions

• LCM of denominators is to be found only while performing addition or subtraction of unlike fractions.
• While multiplying fractions we can change their order, but the product remains the same. (commutative property)
• If a fraction is multiplied by 0, the product is always zero.
• If a fraction is multiplied by 1, the product is the same fraction.
• A fraction is in the lowest term when the only common factor between the numerator and the denominator is 1
• If any of the fraction is a mixed number or a whole number, change it to an improper function and then multiply.

Quiz for Fractions

Your Score: 0 /10

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Real-life problems, working with fractions

Common Core Standards: Grade 5 Number & Operations: Fractions

CCSS.Math.Content.5.NF.B.6

This worksheet originally published in Math Made Easy for 5th Grade by © Dorling Kindersley Limited .

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5th Grade Fractions Word Problems

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Jazz has 4 6/8 wheels of cheese. She was given 7/8 more cheese! How much cheese does she have now?

Bob has 2 1/8 sheets of metal. To make a roof Bob needs to use 4/5 of the sheets of metal. How many sheets of metal does Bob have after building one roof?

52/30 or 1 11/15

Bralyn has 3 1/3 cupcakes. Kylie took away 7/8 of a cup cake. How many cupcakes does Bralyn have left?

80/21 or 3 17/21

70/24 or 2 11/12

Phelan has 2 5/6 pizzas. He orders 4/5 more of a pizza. How much pizza does he have now? First estimate, then solve.

Estimation: 2

Answer: 3 1/3

Estimation: 12

Answer: 5/12

Estimation: 3

Jacob has 4 1/4 pizzas. He ate 2/3 of the pizzas. How many pizzas does he have left?

51/8 or 6 3/8

3 7/12 or 43/12

You have 3/4 of a bag of dog food. You have one week you have to feed your dog the bag of food. How much do you feed him each day?

Lily had 1/6 of a cake left over from her brothers birthday party. If she split the leftover cake evenly between 3 people how much of the cake would each person get?

Kylie has a dozen donuts and Lily has 1/4 of half a dozen. How many donuts do they have all together?

Allie has 2/3 of a candy bar and wants to split it among two people. How much of the candy bar do they each get?

Lily had a dozen cupcakes. Kylie asked for 1/2 of them but Lily said no. When lily left, Kylie took 1/2 anyway. How many cupcakes did Kylie take?

Wyatt had 1/3 of a steak and split it with his dad. How much steak did Wyatt’s dad eat?

Allie needs 3/4 cup of ketchup for a meatloaf recipe. She has an almost empty bottle which contains 1/4 cup of ketchup, another two bottles with 1/3 cup of ketchup in each bottle. Does she have enough for the recipe? How much does she have total?

yes, 11/12 cup

no, 2/3 cup

no, 1/2 cup

Miss Marsh was baking cookies and wanted to triple the batch. One batch calls for 2/3 cup of sugar. How many cups of sugar will she use for all three batches?

Avery was making brownies. The recipe made 24 brownies but she only wanted to make 12. The recipe called for 1 1/2 cups milk. How much milk will she need to make 12 brownies?

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