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

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

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

\(\frac{1}{2}\div3=\frac{1}{6}\)

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

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

\(\frac{1}{4}\div2=\frac{1}{8}\)

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

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

\(\frac{1}{3}\div5=\frac{1}{15}\)

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

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

\(\frac{1}{5}\div4=\frac{1}{20}\)

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

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

\(\frac{1}{6}\div3=\frac{1}{18}\)

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

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

\(4\div\frac{1}{2}=8\)

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

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

\(3\div\frac{1}{4}=12\)

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

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

\(5\div\frac{1}{3}=15\)

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

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

\(2\div\frac{1}{5}=10\)

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

Check: \(36\times\frac{1}{6}=6\)

\(6\div\frac{1}{6}=36\)

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

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

\(\frac{1}{8}\div3=\frac{1}{24}\)

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

\(\frac{1}{4}\div3=\frac{1}{12}\)

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.

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

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

\(\frac{1}{4}\div2>\frac{1}{4}\div3\)

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

\(2\div\frac{1}{3}=6\)

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

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

Check: \(20\times\frac{1}{4}=\frac{20}{4}=5\) yards.

20 pieces

\(\frac{1}{3}\div6=\frac{1}{3\times6}=\frac{1}{18}\).

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

\(\frac{1}{18}\) of the pan

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

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

(a) 24 laps; (b) 6 laps

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