### A whole number multiplied by a fraction

Multiplication by a whole number is simply repeated addition. For example, we know that 5 × 3 means that we add 3 + 3 + 3 + 3 + 3 and obtain 15.

Similarly, $$8×\dfrac{1}{4}$$ is the same as $$\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4} +\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}=2$$.

This can be found by writing

$$8×\dfrac{1}{4}=\dfrac{8}{4}=2$$

We can also think of this as 8 lots of $$\dfrac{1}{4}$$.

Thus 8 lots of $$\dfrac{1}{4}$$, 8 × $$\dfrac{1}{4}$$ and $$\dfrac{8}{4}$$ are all the same thing, and each is equal to 2.

#### Example 1

1. $$20 ×\dfrac{3}{4}$$
2. $$30 ×\dfrac{5}{6}$$

#### Solution

1. \begin{align}20×\dfrac{3}{4}&=\dfrac{20×3}{4}\\\\ &=\dfrac{60}{4}\\\\ &=15\end{align}
2. \begin{align}30×\dfrac{5}{6}&=\dfrac{30×5}{6}\\\\ &=\dfrac{150}{6}\\\\ &=25\end{align}