5th Grade Multiplying Fractions and Mixed Numbers Worksheet Solutions (PDF)

Write the whole number 4 as \(\frac{4}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{4}{1} \times \frac{1}{5} = \frac{4 \times 1}{1 \times 5} = \frac{4}{5}\).

\(\frac{4}{5}\)

Write the whole number 3 as \(\frac{3}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{3}{1} \times \frac{2}{7} = \frac{3 \times 2}{1 \times 7} = \frac{6}{7}\).

\(\frac{6}{7}\)

Write the whole number 5 as \(\frac{5}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{5}{1} \times \frac{3}{4} = \frac{5 \times 3}{1 \times 4} = \frac{15}{4}\).

Write as a mixed number: \(\frac{15}{4} = 3\frac{3}{4}\).

\(3\frac{3}{4}\)

Split 15 into 3 equal parts: \(15 \div 3 = 5\). Take 2 parts: \(2 \times 5 = 10\).

Check: \(\frac{2}{3} \times 15 = \frac{30}{3} = 10\).

\(10\)

Write the whole number 20 as \(\frac{20}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{3}{4} \times \frac{20}{1} = \frac{3 \times 20}{4 \times 1} = \frac{60}{4}\).

Simplify: \(\frac{60}{4} = 15\).

\(15\)

Multiply the numerators and multiply the denominators: \(\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}\).

\(\frac{1}{6}\)

Multiply the numerators and multiply the denominators: \(\frac{2}{3} \times \frac{3}{5} = \frac{2 \times 3}{3 \times 5} = \frac{6}{15}\).

Simplify: \(\frac{6}{15} = \frac{2}{5}\).

\(\frac{2}{5}\)

Multiply the numerators and multiply the denominators: \(\frac{3}{4} \times \frac{4}{9} = \frac{3 \times 4}{4 \times 9} = \frac{12}{36}\).

Simplify: \(\frac{12}{36} = \frac{1}{3}\).

\(\frac{1}{3}\)

Multiply the numerators and multiply the denominators: \(\frac{5}{6} \times \frac{3}{10} = \frac{5 \times 3}{6 \times 10} = \frac{15}{60}\).

Simplify: \(\frac{15}{60} = \frac{1}{4}\).

\(\frac{1}{4}\)

The width has 3 of 5 columns shaded and the height has 3 of 4 rows shaded.

\(\frac{3}{5} \times \frac{3}{4} = \frac{9}{20}\)

\(\frac{9}{20}\)

Write the mixed number as improper fraction: \(2\frac{1}{2} = \frac{5}{2}\).

Write the whole number 4 as \(\frac{4}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{5}{2} \times \frac{4}{1} = \frac{5 \times 4}{2 \times 1} = \frac{20}{2}\).

Simplify: \(\frac{20}{2} = 10\).

\(10\)

Write the mixed number as improper fraction: \(1\frac{1}{3} = \frac{4}{3}\).

Multiply the numerators and multiply the denominators: \(\frac{4}{3} \times \frac{3}{4} = \frac{4 \times 3}{3 \times 4} = \frac{12}{12}\).

Simplify: \(\frac{12}{12} = 1\).

\(1\)

Estimate: \(2\frac{3}{4}\) rounds to 3 and \(1\frac{2}{3}\) rounds to 2, so the estimate is \(3 \times 2 = 6\).

Write the mixed numbers as improper fractions: \(2\frac{3}{4} = \frac{11}{4}\) and \(1\frac{2}{3} = \frac{5}{3}\).

Multiply the numerators and multiply the denominators: \(\frac{11}{4} \times \frac{5}{3} = \frac{11 \times 5}{4 \times 3} = \frac{55}{12}\).

Write as a mixed number: \(\frac{55}{12} = 4\frac{7}{12}\).

The exact product is a little less than the estimate of 6, so it is reasonable.

\(4\frac{7}{12}\)

Write the mixed numbers as improper fractions: \(3\frac{1}{2} = \frac{7}{2}\) and \(2\frac{2}{5} = \frac{12}{5}\).

Multiply the numerators and multiply the denominators: \(\frac{7}{2} \times \frac{12}{5} = \frac{7 \times 12}{2 \times 5} = \frac{84}{10}\).

Simplify: \(\frac{84}{10} = \frac{42}{5}\).

Write as a mixed number: \(\frac{42}{5} = 8\frac{2}{5}\).

\(8\frac{2}{5}\)

Multiply the numerators and multiply the denominators: \(\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}\).

\(\frac{3}{8}\)

Maya uses \(\frac{3}{8}\) cup of sugar.

Write the whole number 6 as \(\frac{6}{1}\).

Multiply the numerators and multiply the denominators: \(\frac{6}{1} \times \frac{3}{4} = \frac{6 \times 3}{1 \times 4} = \frac{18}{4}\).

Simplify: \(\frac{18}{4} = \frac{9}{2}\).

Write as a mixed number: \(\frac{9}{2} = 4\frac{1}{2}\).

\(4\frac{1}{2}\)

The jugs hold \(4\frac{1}{2}\) gallons.

Area = length times width.

Write the mixed numbers as improper fractions: \(2\frac{1}{2} = \frac{5}{2}\) and \(1\frac{3}{5} = \frac{8}{5}\).

Multiply the numerators and multiply the denominators: \(\frac{5}{2} \times \frac{8}{5} = \frac{5 \times 8}{2 \times 5} = \frac{40}{10}\).

Simplify: \(\frac{40}{10} = 4\).

\(4\)

The area is \(4\) square feet.

Fraction eaten:

Multiply the numerators and multiply the denominators: \(\frac{2}{5} \times \frac{5}{6} = \frac{2 \times 5}{5 \times 6} = \frac{10}{30}\).

Simplify: \(\frac{10}{30} = \frac{1}{3}\).

\(\frac{1}{3}\)

Fraction still left: \(\frac{5}{6} – \frac{1}{3} = \frac{5}{6} – \frac{2}{6} = \frac{3}{6} = \frac{1}{2}\).

Ethan eats \(\frac{1}{3}\) of the pizza, and \(\frac{1}{2}\) of the pizza is still left.

Write the price as a mixed number: $2.50 is \(2\frac{1}{2}\) dollars.

Write the mixed numbers as improper fractions: \(3\frac{1}{2} = \frac{7}{2}\) and \(2\frac{1}{2} = \frac{5}{2}\).

Multiply the numerators and multiply the denominators: \(\frac{7}{2} \times \frac{5}{2} = \frac{7 \times 5}{2 \times 2} = \frac{35}{4}\).

Write as a mixed number: \(\frac{35}{4} = 8\frac{3}{4}\).

\(8\frac{3}{4}\)

\(8\frac{3}{4}\) dollars is $8.75.

Priya pays $8.75.

Cups needed:

Write the mixed numbers as improper fractions: \(1\frac{2}{3} = \frac{5}{3}\) and \(2\frac{1}{2} = \frac{5}{2}\).

Multiply the numerators and multiply the denominators: \(\frac{5}{3} \times \frac{5}{2} = \frac{5 \times 5}{3 \times 2} = \frac{25}{6}\).

Write as a mixed number: \(\frac{25}{6} = 4\frac{1}{6}\).

\(4\frac{1}{6}\)

Cost: \(\frac{25}{6} \times \frac{3}{2} = \frac{75}{12} = 6\frac{3}{12} = 6\frac{1}{4}\), which is $6.25.

Diego needs \(4\frac{1}{6}\) cups of raisins, and they cost $6.25.