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

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This multiply fraction whole answers for 4th Grade covers multiplying a fraction by a whole number (Common Core 4.NF.B.4a, 4.NF.B.4b, 4.NF.B.4c), with a free PDF to print.

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

Multiply fraction whole answers: exercises 1 to 10

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

Exercises 11 and up

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.

Key facts behind this multiply fraction whole answers

Key facts

A fraction a/b is a multiple of the unit fraction 1/b, so a/b = a x 1/b.
n x (a/b) = (n x a)/b. Multiply the whole number by the numerator and keep the denominator.
Repeated jumps on a number line show the same product.
Write improper fraction products as mixed numbers when it helps.
Equal groups in word problems signal fraction times whole number.

How to use this multiply fraction whole 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.

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