Simplifying Ratios


  • Ratios show the quantitative relationship between two amounts.

  • Just like fractions, we can simplify ratios to their lowest term. This makes ratios easier to understand and to work with.

  • To simplify a ratio we divide each part by a common factor. Therefore we need to find the highest common factor of the numbers that make up the ratio.

For example

Simplify: 10: 15: 20

The first thing we need to do is find the highest common factor of these numbers.

Factors of 10 : 1, 2, 5

Factors of 15: 1,3,5,15

Factors of 20: 1, 2,4,5,10,20

If we look at this list we can see 5 is the highest common factor (HCF), therefore we will divide each number by 5. This will give means:




Caroline and Rachel share some money in a ratio of 4:5 Caroline gets £20, how much will Rachel get?
Share $40 in a ratio of 3:2:5
Your answer should include: $12 / $8 / $20
Simplify 12:18:6