Skill: Multiply a fraction by a whole number

To multiply a fraction by a whole number, think of the whole number as telling you how many equal groups of the fraction to find.

Example

Find:

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

Step 1: Write the fraction as repeated addition.

Three groups of $\frac{2}{5}$ are:

$$\frac{2}{5}+\frac{2}{5}+\frac{2}{5}$$

Step 2: Keep the denominator the same.

The denominator $5$ tells the size of the parts. There are still fifths, so the denominator stays $5$.

Step 3: Multiply the numerator by the whole number.

There are $3$ groups of $2$ fifths:

$$3 \times 2=6$$

So:

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

Step 4: Understand the result.

Six fifths is one whole and one fifth:

$$\frac{6}{5}=1\frac{1}{5}$$

Therefore:

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

On a number line, you could start at $0$ and make three equal jumps of $\frac{2}{5}$: first to $\frac{2}{5}$, then to $\frac{4}{5}$, and finally to $\frac{6}{5}$.