### Dividing by a whole number

We have seen how to divide a whole number by a whole number.

For example, $$7÷3=\dfrac{7}{3}=2\dfrac{1}{3}$$.

Thus dividing by 3 gives the same answer as finding $$7×\dfrac{1}{3}=\dfrac{7}{3}$$.

In general, for whole numbers m and n, dividing m by n is the same as multiplying m by $$\dfrac{1}{n}$$.

$$m\div n=m\times\dfrac{1}{n}$$

The fraction $$\dfrac{1}{n}$$ is called the reciprocal of n.

### Dividing a fraction by a whole number

This same idea can be used when dividing a fraction by a whole number.

For example, $$\dfrac{3}{5}\div6$$ means that we take $$\dfrac{3}{5}$$ and divide it into 6 equal parts.

The first diagram shows $$\dfrac{3}{5}$$ and the second diagram shows this area divided into six equal parts. The dark shaded area represents $$\dfrac{3}{5}\div6$$ and $$\dfrac{3}{30}$$.

We note that $$\dfrac{3}{5}\times\dfrac{1}{6}=\dfrac{3}{30}$$, so the rule for multiplying by the reciprocal also holds.