 What you need to know

Things to remember:

• Percentages are really just dividing by 100, so we can write it as a fraction with a denominator of 100.
• Sometimes you can simplify your fraction.

First, let’s break up the word “percent” into “per” and “cent”.

per – “for every” or “out of”

cent – 100 (Century = 100 years)

So, if we put these together, then “percent” means “for every 100” or “out of 100”. Writing “percent” takes waaaaaaaay too long, so we use the symbol %.

10% – 10 percent

25% – 25 percent

47% – 47 percent

So, something like 47% just means “47 out of every 100”. We could show this percentage by cutting a block into 100 pieces and taking 47 of them: So really, a percentage is actually just dividing by 100!

$$47\%=47\div100$$

But, do we know any other ways of writing a division?… Yes! We know that divisions and fractions are the same thing. The number being divided goes on top, and the number we are dividing by goes on the bottom.

$$47\%=47\div100=\frac{47}{100}$$

So really, to write a percentage as a fraction, we just write the percentage over 100!

$$4\%=\frac{4}{100}$$

$$23\%=\frac{23}{100}$$

$$146\%=\frac{146}{100}$$

Sometimes we can simplify fractions, so let’s look at 10%.

$$10\%=\frac{10}{100}$$

We have seen this as a fraction before and know how to simplify it.

$$\frac{10}{100}=\frac{1}{10}$$

$$10\%=\frac{1}{10}$$

There are quite a few percentages less than 100% that can be simplified, and it is good being able to recognise some of the important ones.

Percentage                 Fraction

100%                           1

90%                             $\dfrac{9}{10}$

80%                             $\dfrac{4}{5}$

75%                             $\dfrac{3}{4}$

70%                             $\dfrac{7}{10}$

60%                             $\dfrac{3}{5}$

50%                             $\dfrac{1}{2}$

40%                             $\dfrac{2}{5}$

30%                             $\dfrac{3}{10}$

25%                             $\dfrac{1}{4}$

20%                             $\dfrac{1}{5}$

10%                             $\dfrac{1}{10}$

5%                               $\dfrac{1}{20}$

0%                               0

Example Questions

$$59\%=59\div100=\frac{59}{100}$$

$$59\%=\frac{59}{100}$$

$$25\%=25\div100=\frac{25}{100}$$

$$\frac{25}{100}=\frac{1}{4}$$

$$25\%=\frac{1}{4}$$