4th Grade Multiplying a Fraction by a Whole Number Worksheet Solutions (PDF)

4th Grade math worksheet solutions: Multiplying a Fraction by a Whole Number – Maths PDF

Use this answer key to check each problem on the worksheet. Every solution shows the multiplication of the whole number and the numerator, plus the conversion to a mixed number when it is needed.

Grade 4 · Common Core State Standards: 4.NF.B.4a, 4.NF.B.4b, 4.NF.B.4c

Exercise 1 – Three fourths

Three fourths is 3 pieces of one fourth.

Answer: \(\frac{3}{4} = 3 \times \frac{1}{4}\).

Exercise 2 – Five sixths

\(\frac{5}{6} = 5 \times \frac{1}{6}\).

As a sum: \(\frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6}\).

Answer: \(5 \times \frac{1}{6}\).

Exercise 3 – Four fifths

\(4 \times 1 = 4\), and the denominator stays 5.

Answer: \(\frac{4}{5}\).

Exercise 4 – Three groups of two fifths

\(3 \times 2 = 6\), so the product is \(\frac{6}{5}\).

\(\frac{6}{5}\) = \(1\frac{1}{5}\).

6 fifths in all.

Answer: \(\frac{6}{5}\) = \(1\frac{1}{5}\).

Exercise 5 – Two groups of three eighths

\(2 \times 3 = 6\), so \(\frac{6}{8}\).

Answer: \(\frac{6}{8}\).

Exercise 6 – Five thirds

\(5 \times 1 = 5\), so \(\frac{5}{3}\).

\(5 \div 3 = 1\) remainder 2.

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

Exercise 7 – Four groups of three tenths

\(4 \times 3 = 12\), so \(\frac{12}{10}\).

\(12 \div 10 = 1\) remainder 2.

Answer: \(1\frac{2}{10}\).

Exercise 8 – A whole number answer

\(6 \times 2 = 12\), so \(\frac{12}{3}\).

\(12 \div 3 = 4\).

Answer: 4.

Exercise 9 – Three groups of five sixths

\(3 \times 5 = 15\), so \(\frac{15}{6}\).

\(15 \div 6 = 2\) remainder 3.

Answer: \(2\frac{3}{6}\).

Exercise 10 – Seven groups of three fourths

\(7 \times 3 = 21\), so \(\frac{21}{4}\).

\(21 \div 4 = 5\) remainder 1.

Answer: \(5\frac{1}{4}\).

Exercise 11 – Number line jumps

Each jump is \(\frac{3}{8}\). The jumps land at \(\frac{3}{8}\), \(\frac{6}{8}\), \(\frac{9}{8}\) and \(\frac{12}{8}\).

The last jump lands at \(\frac{12}{8}\).

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

Answer: \(\frac{12}{8} = 1\frac{4}{8}\).

Exercise 12 – Complete the product

\(8 \times 3 = 24\), so \(\frac{24}{12}\).

\(24 \div 12 = 2\).

Answer: \(\frac{24}{12} = 2\).

Exercise 13 – Two ways to write nine fourths

Nine fourths is 9 pieces of \(\frac{1}{4}\): \(9 \times \frac{1}{4}\).

Also \(3 \times \frac{3}{4} = \frac{9}{4}\).

Answer: \(9 \times \frac{1}{4}\) and \(3 \times \frac{3}{4}\).

Exercise 14 – Nine groups of two fifths

\(9 \times 2 = 18\), so \(\frac{18}{5}\).

\(18 \div 5 = 3\) remainder 3.

Answer: \(3\frac{3}{5}\).

Exercise 15 – Glasses of milk

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

\(15 \div 4 = 3\) remainder 3.

5 groups of \(\frac{3}{4}\) cup.

Answer: \(3\frac{3}{4}\) cups.

Exercise 16 – Sugar for cookies

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

\(8 \div 3 = 2\) remainder 2.

Answer: \(2\frac{2}{3}\) cups.

Exercise 17 – Training runs

\(6 \times \frac{3}{8} = \frac{18}{8}\).

\(18 \div 8 = 2\) remainder 2.

Answer: \(2\frac{2}{8}\) miles.

Exercise 18 – Ribbon for friends

\(4 \times \frac{5}{6} = \frac{20}{6}\).

\(20 \div 6 = 3\) remainder 2.

Answer: \(3\frac{2}{6}\) yards.

Exercise 19 – Juice for glasses

Juice needed: \(6 \times \frac{3}{4} = \frac{18}{4} = 4\frac{2}{4}\) cups.

Compare with 5 cups: \(5 = \frac{20}{4}\) and \(\frac{20}{4} – \frac{18}{4} = \frac{2}{4}\).

Answer: Yes, enough. \(\frac{2}{4}\) cup is left.

Exercise 20 – Peaches at the market

Noah: \(7 \times \frac{3}{4} = \frac{21}{4}\). Mei: \(5 \times \frac{3}{4} = \frac{15}{4}\).

Together: \(\frac{21}{4} + \frac{15}{4} = \frac{36}{4} = 9\).

Check: \(12 \times \frac{3}{4} = \frac{36}{4} = 9\).

Answer: 9 pounds.

All Grade 4 chapters: Grade 4 math.

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