5th Grade Dividing Unit Fractions and Whole Numbers Worksheet Solutions (PDF)
This divide unit fractions answers for 5th Grade 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.
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
Divide unit fractions answers: exercises 1 to 10
Exercise 1 – Half divided by 3
Cut the unit fraction \(\frac{1}{2}\) into 3 equal pieces. The denominator becomes \(2\times3=6\).
Check: \(\frac{1}{6}\times3=\frac{3}{6}=\frac{1}{2}\)
\(\frac{1}{2}\div3=\frac{1}{6}\)
Exercise 2 – Fourth divided by 2
Cut the unit fraction \(\frac{1}{4}\) into 2 equal pieces. The denominator becomes \(4\times2=8\).
Check: \(\frac{1}{8}\times2=\frac{2}{8}=\frac{1}{4}\)
\(\frac{1}{4}\div2=\frac{1}{8}\)
Exercise 3 – Third divided by 5
Cut the unit fraction \(\frac{1}{3}\) into 5 equal pieces. The denominator becomes \(3\times5=15\).
Check: \(\frac{1}{15}\times5=\frac{5}{15}=\frac{1}{3}\)
\(\frac{1}{3}\div5=\frac{1}{15}\)
Exercise 4 – Fifth divided by 4
Cut the unit fraction \(\frac{1}{5}\) into 4 equal pieces. The denominator becomes \(5\times4=20\).
Check: \(\frac{1}{20}\times4=\frac{4}{20}=\frac{1}{5}\)
\(\frac{1}{5}\div4=\frac{1}{20}\)
Exercise 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: \(\frac{1}{18}\times3=\frac{3}{18}=\frac{1}{6}\)
\(\frac{1}{6}\div3=\frac{1}{18}\)
Exercise 6 – Four wholes in halves
Each whole holds 2 pieces of size \(\frac{1}{2}\). For 4 wholes, multiply: \(4\times2=8\).
Check: \(8\times\frac{1}{2}=4\)
\(4\div\frac{1}{2}=8\)
Exercise 7 – Three wholes in fourths
Each whole holds 4 pieces of size \(\frac{1}{4}\). For 3 wholes, multiply: \(3\times4=12\).
Check: \(12\times\frac{1}{4}=3\)
\(3\div\frac{1}{4}=12\)
Exercise 8 – Five wholes in thirds
Each whole holds 3 pieces of size \(\frac{1}{3}\). For 5 wholes, multiply: \(5\times3=15\).
Check: \(15\times\frac{1}{3}=5\)
\(5\div\frac{1}{3}=15\)
Exercise 9 – Two wholes in fifths
Each whole holds 5 pieces of size \(\frac{1}{5}\). For 2 wholes, multiply: \(2\times5=10\).
Check: \(10\times\frac{1}{5}=2\)
\(2\div\frac{1}{5}=10\)
Exercise 10 – Six wholes in sixths
Each whole holds 6 pieces of size \(\frac{1}{6}\). For 6 wholes, multiply: \(6\times6=36\).
Check: \(36\times\frac{1}{6}=6\)
\(6\div\frac{1}{6}=36\)
Exercises 11 and up
Exercise 11 – Check with multiplication
Multiply the denominator by 3: \(8\times3=24\), so the quotient is \(\frac{1}{24}\).
Check: \(\frac{1}{24}\times3=\frac{3}{24}=\frac{1}{8}\).
\(\frac{1}{8}\div3=\frac{1}{24}\)
Exercise 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 \(\frac{1}{12}\).
\(\frac{1}{4}\div3=\frac{1}{12}\)
Exercise 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.
Exercise 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 \(\frac{1}{8}>\frac{1}{12}\).
\(\frac{1}{4}\div2>\frac{1}{4}\div3\)
Exercise 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.
\(2\div\frac{1}{3}=6\)
Exercise 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
Exercise 17 – Ribbon pieces
\(5\div\frac{1}{4}=5\times4=20\).
Check: \(20\times\frac{1}{4}=\frac{20}{4}=5\) yards.
20 pieces
Exercise 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
Exercise 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
Exercise 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 divide unit fractions answers
- A unit fraction has a numerator of 1, like 1/4 or 1/8.
- 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.
- Check any quotient by multiplying it by the divisor to get the dividend.
- Bar models and number lines show how many pieces there are.
How to use this divide unit fractions answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
Download the divide unit fractions answers as a PDF with the button below and keep it with your notes.
Download the divide unit fractions answers as a PDF with the button below and keep it with your notes.
Download the divide unit fractions answers as a PDF with the button below and keep it with your notes.
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5th Grade Dividing Unit Fractions and Whole Numbers Worksheet Solutions
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