IGCSE Maths / Ratios and percentages
Sharing in a ratio revision notes
Edexcel International GCSE Maths (4MA1), chapter 2: Ratios and percentages, specification point 1.7b. Free lesson.
Watch the video lesson · IGCSE Maths past papers
To share an amount in a ratio, find the value of one part, then multiply it by each share. If two ratios overlap, match the shared quantity first so you can join them into one ratio.
Find the value of one part
The numbers in a ratio tell you how many equal parts each share receives. Add the ratio numbers to find the total number of parts, then divide the whole amount by this total. This gives the value of one part. For 3 : 5, there are 3 + 5 = 8 parts altogether. Divide by the total parts, not by the number of people sharing.
Share an amount between two people
Once you know one part's value, multiply it by each number in the ratio. The shares should add back to the original amount, which is a useful check.
Share an amount between three people
The method is the same for three or more shares. Keep the ratio in the same order as the quantities named in the question. If you change the order, you assign the parts to the wrong quantities. For cement, sand and gravel in the ratio 1 : 2 : 6, the numbers match that order.
Join two ratios before sharing
When two ratios share a quantity, use that shared quantity to connect them. Make its number the same in both ratios by scaling one ratio, then write the combined ratio. Only then can you find the total parts and share the amount. Do not add all four numbers from the two ratios. That counts the shared quantity twice. For A : B = 3 : 4 and B : C = 2 : 5, double the second ratio so B is 4 in both.
Answer the exact question
Read what the question asks for before finishing. If it asks how much more one person receives, calculate both shares and subtract the smaller from the larger. For £840 shared in the ratio 2 : 5, one part is £840 ÷ 7 = £120. Dev gets £240 and Eve gets £600, so Eve gets £360 more.