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.

Natalie is baking 2 different batches of cookies. One batch needs \cfrac cup of sugar and the other batch needs \cfrac 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 fractions

Step-by-step guide: Dividing fractions

What are fraction word problems?

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 \cfracof 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.

• 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\: lb of chocolate equally? How many \cfraccup 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\div \cfracand use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac\div \cfrac=\cfracbecause \cfracof \cfracis \cfrac. (In general, \cfrac\div \cfrac=\cfrac\, )

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

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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!

Grade 4 to 6)" width="463" height="211" />

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

Grade 4 to 6)" width="463" height="211" />

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:

1. Determine what operation is needed to solve.
2. Write an equation.
3. Solve the equation.
4. State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators)

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

1. Determine what operation is needed to solve.

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 of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac of a mile in the morning and \cfrac of a mile in the afternoon. How far did Tim run in total?

Determine what operation is needed to solve.

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.

Write an equation.

Solve the equation.

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

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

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

Now you can add the fractions and simplify the answer.

State your answer in a sentence.

Tim ran a total of 1 \cfrac miles.