Multiplying Fractions: Grade 5 Math Worksheet Answer Key – PDF Download

Grade 5 Multiply Worksheet Answer Key: problems 1–5

Problem 1: Division as a fraction

1. \(3 : 5 = \frac{3}{5}\)
2. \(7 : 8 = \frac{7}{8}\)
3. \(11 : 3 = \frac{11}{3}\). Since \(11 = 3 \times 3 + 2\), \(\frac{11}{3} = 3\frac{2}{3}\).

Answers: \(\frac{3}{5}\), \(\frac{7}{8}\), \(3\frac{2}{3}\)

Problem 2: Sharing pizzas

Each pizza is cut into 5 equal slices. A friend takes one slice from each pizza, so each gets 2 slices of size \(\frac{1}{5}\). Also \(2 : 5 = \frac{2}{5}\).

Answer: \(\frac{2}{5}\) of a pizza

Problem 3: Whole number times a unit fraction

Six pieces of size \(\frac{1}{4}\) make \(\frac{6}{4}\). Four fourths fill 1 whole and 2 fourths remain: \(\frac{6}{4} = 1\frac{2}{4} = 1\frac{1}{2}\).

Answer: \(1\frac{1}{2}\)

Problem 4: Fraction of a whole number

1. \(\frac{3}{5} \times 10 = \frac{30}{5} = 6\)
2. \(\frac{5}{8} \times 24 = \frac{120}{8} = 15\)

Answers: 6 and 15

Problem 5: Whole number times a fraction

\(4 \times \frac{3}{8} = \frac{12}{8} = \frac{3}{2} = 1\frac{1}{2}\)

Answer: \(1\frac{1}{2}\)

Grade 5 Multiply Worksheet Answer Key: problems 6–10

Problem 6: A third of a fourth

The overlap is 1 box out of \(4 \times 3 = 12\) boxes. So \(\frac{1}{3} \times \frac{1}{4} = \frac{1}{12}\).

Answer: \(\frac{1}{12}\)

Problem 7: Area model product

Columns: \(\frac{3}{4}\). Rows: \(\frac{2}{5}\). The overlap has 6 of 20 boxes.

\(\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10}\)

Answer: \(\frac{3}{4} \times \frac{2}{5} = \frac{3}{10}\)

Problem 8: Multiplying two fractions

1. \(\frac{3}{5} \times \frac{2}{9} = \frac{3 \times 2}{5 \times 9} = \frac{6}{45} = \frac{2}{15}\)
2. \(\frac{5}{8} \times \frac{4}{15} = \frac{5 \times 4}{8 \times 15} = \frac{20}{120} = \frac{1}{6}\)
3. \(\frac{7}{10} \times \frac{5}{6} = \frac{7 \times 5}{10 \times 6} = \frac{35}{60} = \frac{7}{12}\)

Answers: \(\frac{2}{15}\), \(\frac{1}{6}\), \(\frac{7}{12}\)

Problem 9: Simplify first

1. 8 and 16 share the factor 8; 3 and 9 share 3. \(\frac{8}{9} \times \frac{3}{16} = \frac{1 \times 1}{3 \times 2} = \frac{1}{6}\)
2. 14 and 21 share 7; 5 and 15 share 5. \(\frac{14}{15} \times \frac{5}{21} = \frac{2 \times 1}{3 \times 3} = \frac{2}{9}\)

Answers: \(\frac{1}{6}\) and \(\frac{2}{9}\)

Problem 10: Area of a small rectangle

Area = width \(\times \) height. \(\frac{5}{8} \times \frac{2}{3} = \frac{10}{24} = \frac{5}{12}\). The green part is 10 of 24 boxes.

Answer: \(\frac{5}{12}\text{ ft}^{2}\)

Grade 5 Multiply Worksheet Answer Key: problems 11–15

Problem 11: Patio tiles

\(3\frac{1}{2} = \frac{7}{2}\) and \(2\frac{1}{2} = \frac{5}{2}\). \(\frac{7}{2} \times \frac{5}{2} = \frac{35}{4} = 8\frac{3}{4}\).

Check by splitting the patio: 6 whole squares (\(3 \times 2\)), a strip along the bottom of area \(3 \times \frac{1}{2} = \frac{3}{2}\), a strip along the right of area \(2 \times \frac{1}{2} = 1\), and a corner of area \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\). Total: \(6 + 1\frac{1}{2} + 1 + \frac{1}{4} = 8\frac{3}{4}\).

Answer: \(8\frac{3}{4}\text{ yd}^{2}\)

Problem 12: Greater, less, or equal

1. \(\frac{7}{8}\) is less than 1, so the product shrinks 5: \(\frac{7}{8} \times 5 < 5\).
2. \(1\frac{1}{4}\) is greater than 1: \(4 \times 1\frac{1}{4} > 4\).
3. \(\frac{2}{3}\) is less than 1: \(\frac{2}{3} \times \frac{3}{4} < \frac{3}{4}\).
4. Multiplying by 1 keeps the number: \(1 \times \frac{9}{10} = \frac{9}{10}\).

Answers: less than, greater than, less than, equal to

Problem 13: Scaling bars

\(3 \times \frac{1}{2} = \frac{3}{2} = 1\frac{1}{2}\) and \(3 \times \frac{5}{4} = \frac{15}{4} = 3\frac{3}{4}\).

Since \(\frac{5}{4} > 1\), the product \(3\frac{3}{4}\) is greater than 3. Answer: \(1\frac{1}{2}\) and \(3\frac{3}{4}\); the second is greater

Problem 14: Mixed number times whole number

1. \(2\frac{1}{4} = \frac{9}{4}\). \(\frac{9}{4} \times 4 = 9\)
2. \(1\frac{2}{3} = \frac{5}{3}\). \(3 \times \frac{5}{3} = 5\)

Answers: 9 and 5

Problem 15: Mixed number times fraction

1. \(\frac{5}{2} \times \frac{8}{5} = \frac{40}{10} = 4\)
2. \(\frac{3}{4} \times \frac{8}{3} = \frac{24}{12} = 2\)

Answers: 4 and 2

Grade 5 Multiply Worksheet Answer Key: problems 16–20

Problem 16: Two mixed numbers

1. \(\frac{10}{3} \times \frac{9}{5} = \frac{90}{15} = 6\)
2. \(\frac{9}{4} \times \frac{4}{3} = \frac{36}{12} = 3\)

Answers: 6 and 3

Problem 17: Missing factor

1. \(\frac{5}{12}\) is half of \(\frac{5}{6}\), so the factor is \(\frac{1}{2}\). Check: \(\frac{5}{6} \times \frac{1}{2} = \frac{5}{12}\).
2. The denominator 4 became 8 and the numerator 3 became 9: the factor is \(\frac{3}{2}\). Check: \(\frac{3}{4} \times \frac{3}{2} = \frac{9}{8}\).

Answers: \(\frac{1}{2}\) and \(\frac{3}{2}\)

Problem 18: Trail mix for hikers

\(5 : 3 = \frac{5}{3} = 1\frac{2}{3}\). Check: \(3 \times 1\frac{2}{3} = 5\).

Answer: \(1\frac{2}{3}\) pounds

Problem 19: Spending part of $36

\(\frac{5}{9} \times 36 = \frac{180}{9} = 20\).

Answer: $20

Problem 20: Piano practice

\(2\frac{1}{4} \times 6 = \frac{9}{4} \times 6 = \frac{54}{4} = \frac{27}{2} = 13\frac{1}{2}\).

Answer: \(13\frac{1}{2}\) hours

Grade 5 Multiply Worksheet Answer Key: problems 21–23

Problem 21: Farmers market tomatoes

\(3\frac{3}{4} = \frac{15}{4}\). \(\frac{2}{3} \times \frac{15}{4} = \frac{30}{12} = \frac{5}{2} = 2\frac{1}{2}\).

Answer: \(2\frac{1}{2}\) pounds

Problem 22: Sandbox area

\(3\frac{3}{4} = \frac{15}{4}\) and \(2\frac{2}{5} = \frac{12}{5}\). \(\frac{15}{4} \times \frac{12}{5} = \frac{180}{20} = 9\).

Answer: \(9\text{ yd}^{2}\)

Problem 23: Pizza night

Given away: \(\frac{3}{5} \times \frac{5}{6} = \frac{1}{2}\) of the pizza. Left: \(\frac{5}{6} – \frac{1}{2} = \frac{1}{3}\) of the pizza. He eats one fourth of it: \(\frac{1}{4} \times \frac{1}{3} = \frac{1}{12}\).

Answer: \(\frac{1}{12}\) of the pizza

How to use this grade 5 multiply worksheet answer key

Read this grade 5 multiply worksheet answer key after trying each problem yourself, and redo any problem you missed.

See every chapter on the Grade 5 math page.