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

Question 1: Write 59% as a fraction.

Answer

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

 

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

Question 2: Write 25% as a fraction.

Answer

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

 

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

 

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