Expressing numbers as fractions and percentages

Out of a form group of 20 people, five people have chosen to take Art at GCSE. What fraction of the class will be taking Art GCSE?

There are five people out of 20 in total. We can write this as \(\frac {5} {20}\).

This fraction can be simplified by dividing the numerator and denominator by the same value:

\(\frac {5 \div 5} {20 \div 5}~=~\frac {1} {4}\)

Question

In June it rains for eight days. What fraction of the month did it rain?

For example, we can’t compare a time in minutes with a number of hours. We must first convert the time in hours to minutes.

We normally change to the smaller unit to avoid having to work with decimals.

Johnny is 20 minutes late for a film that is two hours long. What fraction of the film does he miss?

Once you have expressed the quantity as a fraction of another number, this can be converted to a percentage.

In a bunch of 32 grapes, 4 are mouldy. What percentage of the grapes is mouldy?

Out of my £25 pocket money, I spend £7. What percentage is this?

Express as a fraction: \(\frac {7} {25}\)
Use equivalent fractions to get a denominator of 100: \(\frac {7 \times 4} {25 \times 4}~=~\frac {28} {100}\)
Write as a percentage: 28%

A fish tank is home to 15 fish, after a year the fish have bred and there are now 20 fish. By what percentage has the number of fish increased?

Calculate the change: 20 – 15 = 5
Express the change as a percentage of the original value: \(\frac {5} {15}~=~\frac {1} {3}~=~{0.333}~=~{33.3\percent}~{increase}\)

On Monday there were 45 chocolates in a box. By Friday there were only 12. Work out the percentage change.

Calculate the change: 45 – 12 = 33
Express the change as a percentage of the original value: \(\frac {33} {45}~=~{0.7333333333}~=~{73.3\percent}~{decrease}(to~one~decimal~place)\)