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!



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.



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




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


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



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

Question 1: Write 59% as a fraction.





Question 2: Write 25% as a fraction.