5th Grade Dividing Unit Fractions and Whole Numbers Worksheet Answer Key (PDF)

$5th grade dividing fractions worksheet answers – Maths PDF$

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This 5th grade dividing fractions worksheet answers 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 answer key helps fifth grade students and parents check division of unit fractions and whole numbers and see the reasoning.

Topic: Dividing Unit Fractions and Whole Numbers (5th grade)
Content: Step-by-step answers to 20 worksheet problems
Standards: 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fifth grade students and parents check division of unit fractions and whole numbers and see the reasoning. Also, each solution shows the model or the rule, the quotient, and a multiplication check.

The key covers all 20 problems, including the model in problem 5, the number line in problem 15, and the missing number in problem 13. Then, word problem answers use full sentences with units. Also, if your answer differs, check whether the quotient should be bigger or smaller. Then, plan about 15 minutes to compare and fix your work.

Every solution below shows the picture or the multiplication step, then a check. Compare your work with each answer, and fix any problem where your quotient does not multiply back to the dividend.

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

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

1 – Half divided by 3

Cut the unit fraction $\frac{1}{2}$ into 3 equal pieces. The denominator becomes $2\times3=6$.

Check: $\frac{1}{6}\times3=\frac{3}{6}=\frac{1}{2}$

$\frac{1}{2}\div3=\frac{1}{6}$

2 – Fourth divided by 2

Cut the unit fraction $\frac{1}{4}$ into 2 equal pieces. The denominator becomes $4\times2=8$.

Check: $\frac{1}{8}\times2=\frac{2}{8}=\frac{1}{4}$

$\frac{1}{4}\div2=\frac{1}{8}$

3 – Third divided by 5

Cut the unit fraction $\frac{1}{3}$ into 5 equal pieces. The denominator becomes $3\times5=15$.

Check: $\frac{1}{15}\times5=\frac{5}{15}=\frac{1}{3}$

$\frac{1}{3}\div5=\frac{1}{15}$

4 – Fifth divided by 4

Cut the unit fraction $\frac{1}{5}$ into 4 equal pieces. The denominator becomes $5\times4=20$.

Check: $\frac{1}{20}\times4=\frac{4}{20}=\frac{1}{5}$

$\frac{1}{5}\div4=\frac{1}{20}$

5 – Sixth divided by 3 with a model

Cut the unit fraction $\frac{1}{6}$ into 3 equal pieces. The denominator becomes $6\times3=18$.

Check: $\frac{1}{18}\times3=\frac{3}{18}=\frac{1}{6}$

Eighteen small pieces fit in the whole bar.

$\frac{1}{6}\div3=\frac{1}{18}$

Worksheet problem 6 and after

6 – Four wholes in halves

Each whole holds 2 pieces of size $\frac{1}{2}$. For 4 wholes, multiply: $4\times2=8$.

Check: $8\times\frac{1}{2}=4$

$4\div\frac{1}{2}=8$

7 – Three wholes in fourths

Each whole holds 4 pieces of size $\frac{1}{4}$. For 3 wholes, multiply: $3\times4=12$.

Check: $12\times\frac{1}{4}=3$

$3\div\frac{1}{4}=12$

Count the parts: 12 fourths in 3 wholes.

8 – Five wholes in thirds

Each whole holds 3 pieces of size $\frac{1}{3}$. For 5 wholes, multiply: $5\times3=15$.

Check: $15\times\frac{1}{3}=5$

$5\div\frac{1}{3}=15$

9 – Two wholes in fifths

Each whole holds 5 pieces of size $\frac{1}{5}$. For 2 wholes, multiply: $2\times5=10$.

Check: $10\times\frac{1}{5}=2$

$2\div\frac{1}{5}=10$

10 – Six wholes in sixths

Each whole holds 6 pieces of size $\frac{1}{6}$. For 6 wholes, multiply: $6\times6=36$.

Check: $36\times\frac{1}{6}=6$

$6\div\frac{1}{6}=36$

Worksheet problems 11 and up

11 – Check with multiplication

Multiply the denominator by 3: $8\times3=24$, so the quotient is $\frac{1}{24}$.

Check: $\frac{1}{24}\times3=\frac{3}{24}=\frac{1}{8}$.

$\frac{1}{8}\div3=\frac{1}{24}$

12 – Write the division sentence

The shaded fourth is cut into 3 equal pieces. The whole now has $4\times3=12$ equal pieces, so each piece is $\frac{1}{12}$.

Each small piece is one twelfth.

$\frac{1}{4}\div3=\frac{1}{12}$

13 – Find the missing number

The quotient 28 is $7\times4$, so the unit fraction is $\frac{1}{4}$. Check: $7\div\frac{1}{4}=7\times4=28$.

$7\div\frac{1}{4}=28$, so the missing number is 4.

14 – Compare two quotients

$\frac{1}{4}\div2=\frac{1}{8}$ and $\frac{1}{4}\div3=\frac{1}{12}$.

Eighths are bigger pieces than twelfths, so $\frac{1}{8}>\frac{1}{12}$.

$\frac{1}{4}\div2>\frac{1}{4}\div3$

15 – Jumps on a number line

Make jumps of $\frac{1}{3}$ from 0 to 2. Each whole has 3 jumps, so 2 wholes have $2\times3=6$ jumps.

Six jumps reach 2.

$2\div\frac{1}{3}=6$

Worksheet problem 16 and after

16 – Trail mix for four

Divide $\frac{1}{2}\div4$: $2\times4=8$, so each friend gets $\frac{1}{8}$ pound.

Check: $\frac{1}{8}\times4=\frac{4}{8}=\frac{1}{2}$.

$\frac{1}{8}$ pound

17 – Ribbon pieces

$5\div\frac{1}{4}=5\times4=20$.

Also, check: $20\times\frac{1}{4}=\frac{20}{4}=5$ yards.

20 pieces

18 – Brownie pan

$\frac{1}{3}\div6=\frac{1}{3\times6}=\frac{1}{18}$.

Check: $\frac{1}{18}\times6=\frac{6}{18}=\frac{1}{3}$.

$\frac{1}{18}$ of the pan

19 – Laps around the track

(a) $3\div\frac{1}{8}=3\times8=24$ laps.

(b) $24-18=6$ laps.

(a) 24 laps; (b) 6 laps

20 – Paint for a sign

Each jar: $\frac{1}{2}\div3=\frac{1}{6}$ gallon.

Two jars: $2\times\frac{1}{6}=\frac{2}{6}=\frac{1}{3}$ gallon.

$\frac{1}{3}$ gallon

Key facts behind this 5th grade dividing fractions worksheet answers

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 answers

Students compare only the final fraction. Instead, check the multiplication check line to confirm. Slow down at that step and check it twice.
Students skip the models in the key. Instead, the models show why the denominator grows or the count grows.
Students answer problem 18 with one sixth. The share is of the whole pan, so use one third divided by six.
Students forget units in word problems. Also, answers include pounds, pieces, laps, or gallons. Slow down at that step and check it twice.

How to use these solutions

Multiply your quotient by the divisor and compare with the dividend. Also, this check works for every problem.
Redo each missed problem with a strip. Then, the strip shows the size of each piece. Repeat this habit on every problem for the best results.
Parents can ask the child to explain why dividing by one half doubles a number. Repeat this habit on every problem for the best results.

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

5th grade dividing fractions worksheet answers: frequently asked questions

What are the answers to problems 6 to 10?

Four divided by one half is 8, three divided by one fourth is 12, five divided by one third is 15, two divided by one fifth is 10, and six divided by one sixth is 36. Each is the whole number times the denominator.

How does the key find the missing number in problem 13?

Seven divided by a unit fraction equals 28. Since 7 times the denominator is 28, the denominator is 4. So the missing unit fraction is one fourth, and 7 divided by one fourth is 28.

How much paint does Ethan use in problem 20?

One half gallon shared equally among 3 jars puts one sixth gallon in each jar. He uses 2 jars, so he uses two sixths, which is one third of a gallon. A quick check like this takes only a few seconds and prevents most errors.

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