## Content description

Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)

### Elaboration

• investigating multiplication of fractions and decimals, using strategies including patterning and multiplication as repeated addition, with both concrete materials and digital technologies, and identifying the processes for division as the inverse of multiplication

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

### 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}