IGCSE Maths / Ratios and percentages
Ratio and fraction links revision notes
Edexcel International GCSE Maths (4MA1), chapter 2: Ratios and percentages, specification point 1.7a. Free lesson.
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Ratios and fractions describe the same parts in different ways. You need to simplify ratios and choose the correct denominator when changing between ratios and fractions.
How to simplify a ratio
To simplify a ratio, divide both numbers by the same number. Keep dividing until no number other than 1 divides into both parts. Simplest form means the ratio cannot be reduced any further. To write a ratio in the form 1 : n, divide both sides by the first number.
How to find a share from a ratio
In a ratio of 2 : 3, the whole is made from 2 + 3 = 5 equal parts. So the first share is 2/5 of the whole, not 2/3. The denominator is 5 because it counts every part. For a total of £45, each part is worth £45 ÷ 5 = £9. Priya gets 2 parts, so she gets £18. Sam gets 3 parts, so he gets £27. The fraction 2/3 compares Priya's 2 parts with Sam's 3 parts. It is not Priya's fraction of the total.
Why a ratio can give two fractions
The ratio 2 : 3 gives two valid fractions, depending on what the question compares. To find a share of the whole, use all the parts on the bottom. To compare one share with the other, use the other share's parts on the bottom. Priya's fraction of all the money is 2/5. Priya's share compared with Sam's is 2/3. Both equal £18 in their respective calculations: 2/5 of £45 is £18, and 2/3 of £27 is £18.
How to turn a fraction into a ratio
A fraction of a group gives the number of parts in the named share and the number of parts in the whole. Work out the actual number in that share, then subtract it from the total to find the other share.
Finding a fraction from a ratio
To find the fraction of a whole group represented by one share, add the ratio numbers first. The total number of parts goes on the bottom, and the chosen share goes on the top. For red : blue = 4 : 7, there are 4 + 7 = 11 parts altogether. Blue is 7/11 of the counters.