Common Core (CCSS)5th GradeMath

5.NF.B.7— Dividing Unit Fractions and Whole Numbers

Number & Operations—Fractions · 5.NF.B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

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What this standard means: In this lesson, your child will practice dividing unit fractions by whole numbers and whole numbers by unit fractions. They will read short passages and examples about carrot sticks, granola bars, and garden plots, then decide whether each example shows correct reasoning or a common mistake. The lesson helps children see that division can mean sharing equally or finding how many groups fit. They will check answers by thinking about size, since sharing one small piece among more people makes each share smaller, and counting how many small pieces fit into a whole makes the answer larger. This work builds careful fraction sense and helps children explain why an answer makes sense.

What the standard says, word for word · 5.NF.B.7

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions

Read it at the source: Common Core State Standards

What’s inside

What you get, and who it’s for

Everything below is measured from the actual lesson and the actual file. Nothing here is an estimate.

Time to run: About 31 minutes. 10 min lesson, then 21 min of practice.
In the download: 8 printable pages: the full lesson, the worked examples, the visual models, and 11 practice problems with space to work. An educator answer key is included at the end, so the student pages come first and it is still ready to hand out. The lesson’s worked examples do show their solutions, because that is how they teach.
Question set: The download carries all 11 questions. The page shows 11 of them as a sample.
Question format: Every question is numeric answer. Students show their work on the page.
Assumed before this: Students who are shaky on these will struggle with 5.NF.B.7. Worth a quick check first.
5.G.A.1(5th Grade) Students need to know how division can mean equal sharing or finding how many groups fit, especially with whole numbers. They also need a solid understanding of unit fractions and how partitioning a whole into equal parts changes the size of each part.
Dates: Published August 31, 2026. Not revised since.

The sample intervention

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5.NF.B.7

Fraction Division Fix-It: Carrot Sticks, Granola Bars, and Garden Plots

Divide unit fractions by whole numbers and whole numbers by unit fractions using correct reasoning about equal shares and how many groups fit.

Read the passages and examples below. Two examples show correct work and three show a common mistake: multiplying when you should divide, or flipping the wrong number. For every answer, check the size: sharing one piece among more people makes each piece smaller; counting how many small pieces fit into wholes makes the number bigger.

Start with what you already know about division. Division can show equal sharing or how many groups fit. If 12 carrot sticks are shared among 3 students, each student gets 4 carrot sticks. That is a whole-number division situation.

A unit fraction means one equal part of a whole, like 1/4 or 1/6. When you divide a unit fraction by a whole number, you are splitting one small piece into more equal parts. The parts get smaller, not larger.

For example, 1/2 of a granola bar split among 2 friends makes 2 equal pieces from the half. Each friend gets 1/4 of the whole granola bar, because one half split into 2 equal parts makes fourths.

Worked exampleCorrect work: 1/3 ÷ 3 = 1/9. One third split into 3 equal parts makes ninths; each part is 1/9 of the whole.

Worked exampleIncorrect work: 1/5 ÷ 2 = 2/5. This is wrong because splitting one fifth into 2 equal parts makes smaller pieces. The correct answer is 1/10.

One fifth split into 2 parts

The claimed answer 2/5 is bigger than 1/5. Splitting makes pieces smaller: the correct answer 1/10 is the shortest bar.

When you divide a whole number by a unit fraction, you ask how many unit-fraction pieces fit into the whole. If 3 garden plots are each split into 1/2-plot sections, there are 6 half-plot sections in all.

Worked exampleIncorrect work: 3 ÷ 1/4 = 3/4. This is wrong because 3 contains twelve fourths, so dividing by 1/4 makes the number bigger. The correct answer is 12.

Worked exampleIncorrect work: 3 ÷ 1/2 = 1.5. This is wrong because the student divided by 2 instead of asking how many halves fit. 3 contains six halves, so the correct answer is 6.

How many halves fit in 3?

3 wholes contain six 1/2-size pieces. Dividing by a unit fraction asks how many pieces fit.

Worked exampleCorrect work: 2 ÷ 1/6 = 12. Two wholes each contain six sixths, so twelve sixths fit in all.

A common mistake is to multiply when you should divide, or to flip the wrong number. Careful readers check the story first: Are you sharing one piece among more groups, or counting how many small pieces fit into a whole?

Use the meaning of the problem to choose the operation. Then check whether the answer should be smaller than the original amount or larger than it.

Practice questions

1
Compute: 1/2 ÷ 4 = ?
2
A garden has 3 plots. Each plot is split into 1/3-plot sections. How many 1/3-plot sections are there in all?
3
Error analysis: A student says 1/3 ÷ 2 = 2/3. What is the correct answer?
4
Error analysis: A student says 2 ÷ 1/4 = 1/2 because 2 is cut in half. What is the correct answer?
5
A snack box has 1/2 of a granola bar. The half is shared equally by 4 friends. What fraction of a WHOLE granola bar does each friend get?
6
Compare these two answers. Which is larger: 1/2 ÷ 3 or 1/2 ÷ 6? Enter the larger value.
7
A garden plan says 2 plots are each split into 1/4-plot sections. How many sections are there?
8
Explain the error: A student says 1/4 ÷ 2 = 1/2 because the answer got bigger. What is the correct answer?
9
Error analysis: A student says 3 ÷ 1/3 = 1. What is the correct answer?
10
Explain the mistake: A student says 1/3 ÷ 2 = 2/6 because they multiplied top and bottom by 2. What is the correct answer?
11
Compare these two amounts. Which is larger: 2 ÷ 1/4 or 2 ÷ 1/2? Enter the larger value.

Part of the question set is shown. Generate the whole intervention, freshly themed and with an answer key, for your own class in the product.

Watch for this

Common mistakes

Mixing up division with multiplying or flipping the wrong number: Students often see a fraction in a division problem and try to make the answer bigger, or they reverse the wrong part of the equation. In this skill, the story matters, if you are splitting one unit fraction among more people, each part gets smaller, and if you are finding how many unit-fraction pieces fit into a whole, the answer gets larger.

Vocabulary

Key terms

division: Division can show equal sharing or how many groups fit.
unit fraction: A unit fraction means one equal part of a whole, like 1/4 or 1/6.
equal parts: Equal parts are pieces that are the same size.
whole number: A whole number is a counting number like 3 or 12.

In the classroom

How to use this intervention

Use this worksheet after a brief whole-class review of division meaning, then have students work independently for practice while you circulate and check for the common mistakes named in the directions. With 21 practice minutes, use the last few minutes for partner or small-group error analysis on the questions that ask students to explain the mistake and compare answers.

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Questions educators ask

Educator FAQ

What grade is this worksheet for?

This worksheet is for Grade 5.

Which CCSS standard does it align to?

It aligns to CCSS 5.NF.B.7, which focuses on dividing unit fractions and whole numbers using equal shares and how many groups fit.

Is an answer key included?

Yes, the correct answers are included in the lesson context through the worked examples and answer information.