Skip to main content

About this free course

Download this course

Share this free course

Ratio, proportion and percentages
Ratio, proportion and percentages

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

3 Percentages

3.1 What are percentages?

Percentages are used, particularly in newspaper articles, to indicate fractions (as in ‘64% of the population voted’) or to indicate changes (as in ‘an increase of 4%’).

Percentages often indicate proportions. For example, labels in clothes indicate the various proportions of different yarns in the fabric. ‘Per cent’ means ‘per hundred’ and is denoted by the symbol %. 100% is the same as the whole, or one hundred per hundred.

2 written clothes label with the text '100% cotton' and '60% cotton, 40% polyester'

   100% cotton indicates that the fabric is made entirely from cotton. (100 parts out of 100 parts).

   60% cotton means that    (or 0.6) of the fabric is cotton.

   40% polyester means that    (or 0.4) is polyester.

The percentages on the label should total 100%, just as the corresponding fractions add up to 1, because the total (100%) refers to the whole garment. 60% + 40% = 100%, 0.6 + 0.4 = 1.

Percentages can also be manipulated as either fractions or decimals.

Example 10

A building society offers 90% mortgages to first-time buyers. How much would the Smiths get on a house valued at £150 000?

Answer

They want to find 90% of £150 000. 90% = = 0.9.

  0.9 × 150 000 = 135 000

So the Smiths would get £135 000.