Writing and simplifying ratios
Simplify by dividing every part
A ratio compares amounts.
Divide every part by the same number, and keep going until the only common factor is 1.
- 24 : 36
- the highest common factor of 24 and 36 is 12
- 24 ÷ 12 = 2 and 36 ÷ 12 = 3
- 24 : 36 = 2 : 3
Three parts work the same way: 40 : 60 : 100 = 2 : 3 : 5 (divide by 20). The order matters: 2 : 3 is not the same as 3 : 2.
Units, decimals and fractions
Put both amounts in the same unit first: 45 cm : 2 m = 45 cm : 200 cm = 9 : 40.
Writing 45 : 2 compares centimetres with metres.
With decimals, multiply to get whole numbers, then simplify: 1.2 : 0.8 = 12 : 8 = 3 : 2. With fractions, multiply by a common denominator: 2/3 : 1/4, × 12, gives 8 : 3.
The form 1 : n means divide both parts by the first: 8 : 30 = 1 : 3.75. For n : 1, divide by the second: 30 : 8 = 3.75 : 1.
Ratios and fractions
In the ratio 2 : 5 there are 2 + 5 = 7 parts.
So 2/7 of the whole is the first thing and 5/7 is the second. A common slip is to say the first is 2/5 of the whole: 2/5 compares the parts with each other, not with the total.
Going back: if 3/8 of a group are under 18, the other 5/8 are not, so the ratio is 3 : 5.
Simplify with the ratio tool
In the ratio tab, enter 24 : 36 and simplify it. Then enter 1.2 : 0.8, and then 45 : 200 (45 cm : 2 m in centimetres). Which ratio do you get if you forget to change 2 m to centimetres?
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