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One of the most heavily examined ratio skills in OCR GCSE Mathematics (J560) is sharing a quantity in a given ratio — splitting money, ingredients, sweets or angles into parts that match a ratio. This lesson covers the standard "value of one part" method, working back from a single share to find the total, and the slightly trickier case where you are told the difference between two shares rather than the total. These questions appear on every paper and on both tiers.
This lesson develops AO1 fluency with the sharing method, AO2 reasoning when you check that the shares add back correctly, and AO3 problem-solving when the total or the difference is not handed to you directly.
| Term | Meaning |
|---|---|
| Share in a ratio | Split a total amount so the parts match a given ratio |
| Total parts | The sum of the numbers in the ratio |
| Value of one part | The total divided by the number of parts |
| Difference | How much one share exceeds another, in money or units |
| Whole / total | The complete amount being shared out |
Sharing in a ratio is, at heart, a single idea: the total is made up of a whole number of equal "parts", and the ratio tells you how those parts are distributed. Once you know what one part is worth, every share is just a multiple of it. This is why the "value of one part" method is so dependable — it reduces every sharing question, however it is dressed up, to the same three steps, and it works equally well on the non-calculator and calculator papers.
Almost every sharing question uses the same three steps:
Always finish by checking that the shares add back to the original total — a one-line check that catches arithmetic slips. This check is not optional padding: if your shares do not sum to the starting amount, you know immediately that a single arithmetic slip has crept in, and you can fix it before losing marks. Examiners reward clearly shown method, so write each of the three steps down rather than doing them in your head.
Work out how to share £60 in the ratio 2:3.
Total parts =2+3=5.
Value of one part =60÷5=12, i.e. £12 per part.
The two shares are 2×12=24 and 3×12=36, i.e. £24 and £36.
Check: 24+36=60. Correct.
Answer: £24 and £36.
Share £72 between Aisha and Ben in the ratio 5:3. Work out how much Aisha receives.
Total parts =5+3=8. Value of one part =72÷8=9, i.e. £9.
Aisha has 5 parts: 5×9=45, i.e. £45.
Check: Ben gets 3×9=27, and 45+27=72. Correct.
Answer: £45.
Work out how to share 840 g of flour in the ratio 3:4:5.
Total parts =3+4+5=12. Value of one part =840÷12=70 g.
The shares are 3×70=210 g, 4×70=280 g and 5×70=350 g.
Check: 210+280+350=840. Correct.
Answer: 210 g, 280 g and 350 g.
Common error: dividing the total by the number of terms in the ratio (here 3) instead of the number of parts (here 12). Always add the ratio first.
Sometimes you are told the value of a single share and asked for the total, or for one of the other shares. The total amount is not given, so you cannot start by dividing it — instead you work in the other direction. The trick is that the value of one part can be found from any known share, not just from the total. So reverse the method: find the value of one part from the share you know, then multiply by whatever number of parts the question asks about (the total, or another person's share). This "work back from a known share" idea is one of the most useful problem-solving moves in the whole topic, because it lets you unlock a question even when the total is missing.
Money is shared in the ratio 4:7. The smaller share is £52. Work out the total amount shared.
The smaller share is 4 parts and equals £52, so one part =52÷4=13, i.e. £13.
Total parts =4+7=11, so the total =11×13=143, i.e. £143.
Answer: £143.
In a flapjack recipe, oats and syrup are in the ratio 9:2. A batch uses 360 g of oats. Work out the total mass of oats and syrup.
Oats are 9 parts =360 g, so one part =360÷9=40 g.
Total parts =9+2=11, so the total =11×40=440 g.
Answer: 440 g.
Red, green and blue paint are mixed in the ratio 2:3:5. A decorator uses 750 ml of blue paint. Work out how much green paint is used.
Blue is 5 parts =750 ml, so one part =750÷5=150 ml.
Green is 3 parts: 3×150=450 ml.
Answer: 450 ml of green paint. Notice you do not need the total here — once you know one part from the blue share, you can find any other share directly.
A common twist gives you the difference between two shares instead of the total. This catches a lot of students out, because their instinct is to divide the given number by the total parts — but that only works when the number given is the total. When a difference is given, you must divide by the difference in parts. The reasoning is straightforward: if one person has 7 parts and another has 4, the gap between them is 7−4=3 parts, and that gap is what the "difference" describes. So the difference in money (or units) equals the difference in parts multiplied by the value of one part. Rearranging, the value of one part equals the given difference divided by the difference in parts. Always pause and ask: "Is this number the total, a single share, or the difference?" — your first step depends entirely on the answer.
Two numbers are in the ratio 7:4. The larger number is 24 more than the smaller. Work out both numbers.
Difference in parts =7−4=3 parts, and this equals 24.
Value of one part =24÷3=8.
The numbers are 7×8=56 and 4×8=32.
Check: 56−32=24. Correct.
Answer: 56 and 32.
Common error: dividing 24 by the total parts (11) instead of the difference in parts (3). Read carefully whether the question gives a total or a difference.
In a wildlife park the ratio of deer to foxes is 9:2. There are 63 more deer than foxes. Work out the total number of animals.
The difference in parts is 9−2=7 parts, and that equals 63, so one part =63÷7=9 animals.
Total parts =9+2=11, so the total =11×9=99 animals.
Check: deer =9×9=81, foxes =2×9=18, and 81−18=63. Correct.
Answer: 99 animals.
Priya and Quinn share a prize in the ratio 8:5. Priya receives £96 more than Quinn. Work out the total prize.
Difference in parts =8−5=3 parts, equal to £96, so one part =96÷3=32, i.e. £32.
Total parts =8+5=13, so the total =13×32=416, i.e. £416.
Check: Priya gets 8×32=256, Quinn gets 5×32=160, and 256−160=96. Correct.
Answer: £416.
An inheritance of £9,600 is shared between three children in the ratio 1:2:5. Work out how much more the eldest receives than the youngest.
Total parts =1+2+5=8. Value of one part =9,600÷8=1,200, i.e. £1,200.
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