Multiplying Fractions by Whole Numbers

The Idea

Multiplying a fraction by a whole number means adding that fraction multiple times:

$3 \times \frac{2}{5} = \frac{2}{5} + \frac{2}{5} + \frac{2}{5} = \frac{6}{5} = 1\frac{1}{5}$

The Shortcut

$n \times \frac{a}{b} = \frac{n \times a}{b}$

Multiply the whole number by the numerator. The denominator stays the same.

Examples

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

$5 \times \frac{1}{3} = \frac{5}{3} = 1\frac{2}{3}$

$6 \times \frac{2}{7} = \frac{12}{7} = 1\frac{5}{7}$

Word Problems

Each person eats $\frac{3}{8}$ of a pizza. How much pizza do 4 people eat?

$4 \times \frac{3}{8} = \frac{12}{8} = 1\frac{4}{8} = 1\frac{1}{2} \text{ pizzas}$

Simplifying

Always simplify your final answer:

• $\frac{12}{8} = \frac{3}{2} = 1\frac{1}{2}$ ✅
• Divide numerator and denominator by their GCF

Visual model: Draw a number line from 0 to 2. Show $\frac{2}{5}$ three times by jumping $\frac{2}{5}$ each time. You land at $\frac{6}{5} = 1\frac{1}{5}$.