## What you need to know

Things to remember:

• When we divide a fraction by a whole number, we multiply the denominator by it.

This topic will look at questions like:

What is $\dfrac{24}{2}\div3$?

So, how do you think we can do this? Well, remember, a fraction is just another way of writing a “division” question. So, let’s change that fraction into a division.

$$\frac{24}{2}=24\div2$$

$$\frac{24}{2}\div3=24\div2\div3$$

We have now changed this into a question with two divisions, which we can do!

$$24\div2\div3=12\div3=4$$

So, that wasn’t too bad really, was it? There are two things we need to notice here:

1. $2\times3=6$
2. $24\div6=4$

So, I wonder, can we just “multiply” the two divisions together?

What is $\dfrac{40}{5}\div4$?

Let’s see what our two divisions will be.

$$\frac{40}{5}=40\div5$$

$$\frac{40}{5}\div4=40\div5\div4$$

So, we have $\div5$ and $\div4$. If we “multiply” them we’d have $\div20$. So, our answer should be $40\div20=2$. Let’s see if this works.

$$40\div5\div4 =8\div4=2$$

Success, we can “multiply” our divisions!!! So, how does this help us? Well, we can now write our question as one division.

$$\frac{40}{5}\div4=40\div20$$

But, we can write this division as a fraction.

$$\frac{40}{5}\div4=40\div20=\frac{40}{20}$$

$$\frac{40}{5}\div4=\frac{40}{20}$$

So, really, all we do when we divide a fraction by a whole number is we multiply the denominator by it!

$$\frac{40}{5}\div4=\frac{40}{5\times4}=\frac{40}{20}$$

$$\frac{7}{11}\div5=\frac{7}{11\times5}=\frac{7}{55}$$

$$\frac{15}{8}\div7=\frac{15}{8\times7}=\frac{14}{56}$$

## Example Questions

#### Question 1: What is $\dfrac{14}{9}\div12$?

$$\frac{14}{9}\div12=\frac{14}{9\times12}=\frac{14}{108}$$

This can simplify

$$\frac{14}{9}\div12=\frac{7}{54}$$

#### Question 2: What is $\dfrac{23}{3}\div11$?

$$\frac{23}{3}\div11=\frac{23}{3\times11}=\frac{23}{33}$$