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?

Answer

<em>\frac{14}{9}\div12=\frac{14}{9\times12}=\frac{14}{108}</em>

 

This can simplify

 

<em>\frac{14}{9}\div12=\frac{7}{54}</em>

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

Answer

<em>\frac{23}{3}\div11=\frac{23}{3\times11}=\frac{23}{33}</em>

 

This doesn’t simplify.