5th Grade Dividing Unit Fractions and Whole Numbers Worksheets with Answers (Free PDF)

Q: How do you divide a unit fraction by a whole number?

Multiply the denominator by the whole number. One fifth divided by 2 is one tenth, because 5 times 2 is 10. The numerator stays 1, since you still have one piece, now cut smaller.

Q: How do you divide a whole number by a unit fraction?

Multiply the whole number by the denominator. For 4 divided by one third, think of 4 wholes cut into thirds. Each whole has 3 thirds, so there are 12. A quick check like this takes only a few seconds and prevents most errors.

Q: How do you compare two quotients without finding them?

Think about the size of the pieces. A unit fraction divided by 2 gives bigger pieces than the same fraction divided by 3, so the first quotient is greater. Check by finding both. A quick check like this takes only a few seconds and prevents most errors.

$5th grade dividing fractions worksheet – Maths PDF$

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This 5th grade dividing fractions worksheet covers dividing unit fractions and whole numbers (Common Core 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c), with a free PDF to print.

Key takeaway: This worksheet helps fifth grade students practice dividing unit fractions by whole numbers and whole numbers by unit fractions.

Topic: Dividing Unit Fractions and Whole Numbers (5th grade)
Content: 20 worksheet problems, from easy to challenging
Standards: 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c
Answers: On a separate page, so you can try every worksheet problem first
Format: Free printable PDF, US Letter, black and white

This worksheet helps fifth grade students practice dividing unit fractions by whole numbers and whole numbers by unit fractions. Also, models, number lines, and stories about food, ribbon, and laps show why the answers get smaller or bigger.

There are 20 problems. The first five divide a unit fraction by a whole number, with one model, and the next five divide a whole number by a unit fraction. Then, the middle group checks with multiplication, writes division sentences from models, finds a missing number, and compares quotients. Also, the last six are word problems about trail mix, ribbon, brownies, laps, and paint. Then, allow about 30 minutes.

These 20 problems practice standard 5.NF.B.7: dividing a unit fraction by a whole number and dividing a whole number by a unit fraction. You will use bar models and number lines, check answers with multiplication, and solve story problems.

The problems start with quick one-step divisions and grow to multi-step word problems about food, ribbon, laps and paint. Draw a picture whenever you get stuck.

Grade 5 · Common Core State Standards: 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c

5th grade dividing fractions worksheet: worksheet problems 1 to 10

1 – Half divided by 3

First, find $\frac{1}{2}\div3$.

2 – Fourth divided by 2

Next, find $\frac{1}{4}\div2$.

3 – Third divided by 5

Then, find $\frac{1}{3}\div5$.

4 – Fifth divided by 4

Now, find $\frac{1}{5}\div4$.

5 – Sixth divided by 3 with a model

Also, find $\frac{1}{6}\div3$. The model shows one sixth cut into 3 equal pieces.

One sixth cut into 3 equal pieces.

6 – Four wholes in halves

First, find $4\div\frac{1}{2}$.

7 – Three wholes in fourths

Next, find $3\div\frac{1}{4}$. Use the picture to help.

Three wholes, each cut into fourths.

8 – Five wholes in thirds

Then, find $5\div\frac{1}{3}$.

9 – Two wholes in fifths

Now, find $2\div\frac{1}{5}$.

10 – Six wholes in sixths

Also, find $6\div\frac{1}{6}$.

Worksheet problems 11 and up

11 – Check with multiplication

First, find $\frac{1}{8}\div3$. Then write a multiplication sentence that checks the answer.

12 – Write the division sentence

Next, write a division equation and find the quotient for the model.

One fourth cut into 3 equal pieces.

13 – Find the missing number

Then, find the number that makes the equation true: $7\div\frac{1}{\text{?}}=28$.

14 – Compare two quotients

Now, compare $\frac{1}{4}\div2$ and $\frac{1}{4}\div3$ using >, < or =.

15 – Jumps on a number line

Also, find $2\div\frac{1}{3}$ using the number line.

A number line marked in thirds.

16 – Trail mix for four

First, solve. Maya has $\frac{1}{2}$ pound of trail mix. She shares it equally among 4 friends. How much does each friend get?

17 – Ribbon pieces

Next, solve. Jamal has 5 yards of ribbon. He cuts it into pieces that are each $\frac{1}{4}$ yard long. How many pieces does he make?

18 – Brownie pan

Then, solve. After the bake sale, $\frac{1}{3}$ of a pan of brownies is left. Six students share it equally. What fraction of the whole pan does each student get?

One third of the pan cut into 6 pieces.

Worksheet problem 19 and after

19 – Laps around the track

Now, solve. Priya wants to run 3 miles. One lap around the school track is $\frac{1}{8}$ mile. (a) How many laps is 3 miles? (b) She has finished 18 laps. How many laps are left?

20 – Paint for a sign

Also, solve. Ethan pours $\frac{1}{2}$ gallon of paint equally into 3 jars. He uses 2 jars to paint a sign. How much paint does he use?

Key facts behind this 5th grade dividing fractions worksheet

Key facts

A unit fraction has a numerator of 1, like 1/4 or 1/8.
Also, a unit fraction divided by a whole number n is 1 over (denominator times n).
A whole number divided by a unit fraction 1/b equals the whole number times b.
Then, check any quotient by multiplying it by the divisor to get the dividend.
Bar models and number lines show how many pieces there are.

Common mistakes with this 5th grade dividing fractions worksheet

Students answer a sharing problem with a larger fraction. Instead, if one piece is shared among four people, each gets less than the piece.
Students answer a counting problem with a fraction. Also, counting how many small pieces fit into a whole number gives a whole number.
Students find the fraction of the whole pan when a story only gives the share of the leftover. Instead, multiply the denominators to find the share of the whole.
Students forget the second step in a story. Also, after sharing into jars, use the number of jars the story names.

Tips before you start the worksheet problems

Draw a strip and shade the fraction before you divide. Finally, cutting the shaded part shows the new piece size.
Ask whether your answer should be bigger or smaller than the starting number. Also, this quick check catches wrong operations.
Teachers can ask students to write their own sharing story for one problem. Repeat this habit on every problem for the best results.

Download the 5th grade dividing fractions worksheet as a PDF with the button below and keep it with your notes.

5th grade dividing fractions worksheet: frequently asked questions

How do you divide a unit fraction by a whole number?

Multiply the denominator by the whole number. One fifth divided by 2 is one tenth, because 5 times 2 is 10. The numerator stays 1, since you still have one piece, now cut smaller.

How do you divide a whole number by a unit fraction?

Multiply the whole number by the denominator. For 4 divided by one third, think of 4 wholes cut into thirds. Each whole has 3 thirds, so there are 12. A quick check like this takes only a few seconds and prevents most errors.

How do you compare two quotients without finding them?

Think about the size of the pieces. A unit fraction divided by 2 gives bigger pieces than the same fraction divided by 3, so the first quotient is greater. Check by finding both. A quick check like this takes only a few seconds and prevents most errors.

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