GCSE Maths: Sharing a quantity in a ratio (Higher)
Part of the GCSE Maths ratio and proportion chapter (Higher). Chapter overview · Foundation version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Sharing a quantity in a ratio
Aisha and Ben are given £48 to share in the ratio 3 : 5. This means that for every £3 Aisha gets, Ben gets £5. Aisha gets 3 equal parts and Ben gets 5 equal parts. Before we can work out how much each person gets, we need to know how big one part is. The method has three steps, and the bar below shows why it works.
- Add the parts to find the total number of equal parts: 3 + 5 = 8.
- Divide the amount by the total number of parts to find the value of one part: £48 ÷ 8 = £6.
- Multiply the value of one part by each ratio number: 3 × £6 = £18 and 5 × £6 = £30.
Always check that the shares add up to the total: £18 + £30 = £48.
Three or more shares. The same method works for any number of shares. For the ratio 2 : 3 : 5 there are 2 + 3 + 5 = 10 parts. Money. When the total is in pounds and pence, it can help to work in pence (£7.50 = 750p) or to divide the decimal carefully. Remember to write money answers with two decimal places, for example £4.50.
Part : whole ratios. Sometimes a ratio compares one share with the whole, not with the other share. If the ratio of girls to all the students is 3 : 8, then of every 8 students, 3 are girls and the other 5 are not. So girls : not girls = 3 : (8 − 3) = 3 : 5. Change a part : whole ratio into a part : part ratio by taking the part away from the whole, then share as normal.
Key ideas
- Add the ratio numbers to find the total number of equal parts.
- Divide the amount by the total number of parts to find the value of one part.
- Multiply the value of one part by each ratio number.
- Check: the shares must add up to the total.
- Part : whole ratio, for example 3 : 8, means the other share is 8 − 3 = 5 parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.3 + 5 = 8 parts
- Find the value of one part. £48 is shared into 8 equal parts, so divide it by 8.£48 ÷ 8 = £6 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Aisha: 3 × £6 = £18
Ben: 5 × £6 = £30
Check. Add the shares: £18 + £30 = £48, which is the total £48. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.2 + 3 + 5 = 10 parts
- Find the value of one part. 300 ml is shared into 10 equal parts, so divide it by 10.300 ml ÷ 10 = 30 ml for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Red: 2 × 30 ml = 60 ml
Yellow: 3 × 30 ml = 90 ml
White: 5 × 30 ml = 150 ml
Check. Add the shares: 60 ml + 90 ml + 150 ml = 300 ml, which is the total 300 ml. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.2 + 3 = 5 parts
- Find the value of one part. £7.50 is shared into 5 equal parts, so divide it by 5.£7.50 ÷ 5 = £1.50 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.First share: 2 × £1.50 = £3
Second share: 3 × £1.50 = £4.50
Check. Add the shares: £3 + £4.50 = £7.50, which is the total £7.50. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Change the part : whole ratio into a part : part ratio. Then share 40 in that ratio.
- Find the share of the students who are not girls. The whole is 8 parts and girls are 3 of them, so the rest is the whole take away the girls.8 − 3 = 5 parts
- Write the ratio girls : not girls. Now both numbers are parts, so we can share in this ratio.3 : 5
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.3 + 5 = 8 parts
- Find the value of one part. 40 is shared into 8 equal parts, so divide it by 8.40 ÷ 8 = 5 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Girls: 3 × 5 = 15
Not girls: 5 × 5 = 25
Check. Girls are 38 of 40 = 40 ÷ 8 × 3 = 15. ✓
Watch out. The ratio 3 : 8 is not girls to boys. 8 is the whole group, so boys are 8 − 3 = 5 parts.
Watch out
Do not divide the amount by one of the ratio numbers. To share £48 in the ratio 3 : 5, divide by 8 (the total number of parts), not by 3 or 5. And check that your shares add up to the original amount.Exercise 15C Sharing in a ratio
Non-calculatorKey words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.1 + 4 = 5 parts
- Find the value of one part. £20 is shared into 5 equal parts, so divide it by 5.£20 ÷ 5 = £4 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.1 part: 1 × £4 = £4
4 parts: 4 × £4 = £16
Check. Add the shares: £4 + £16 = £20, which is the total £20. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.2 + 5 = 7 parts
- Find the value of one part. £35 is shared into 7 equal parts, so divide it by 7.£35 ÷ 7 = £5 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.2 parts: 2 × £5 = £10
5 parts: 5 × £5 = £25
Check. Add the shares: £10 + £25 = £35, which is the total £35. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.3 + 1 = 4 parts
- Find the value of one part. 48 kg is shared into 4 equal parts, so divide it by 4.48 kg ÷ 4 = 12 kg for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.3 parts: 3 × 12 kg = 36 kg
1 part: 1 × 12 kg = 12 kg
Check. Add the shares: 36 kg + 12 kg = 48 kg, which is the total 48 kg. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.5 + 7 = 12 parts
- Find the value of one part. 72 is shared into 12 equal parts, so divide it by 12.72 ÷ 12 = 6 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.5 parts: 5 × 6 = 30
7 parts: 7 × 6 = 42
Check. Add the shares: 30 + 42 = 72, which is the total 72. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.2 + 3 = 5 parts
- Find the value of one part. £90 is shared into 5 equal parts, so divide it by 5.£90 ÷ 5 = £18 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.2 parts: 2 × £18 = £36
3 parts: 3 × £18 = £54
Check. Add the shares: £36 + £54 = £90, which is the total £90. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.4 + 5 = 9 parts
- Find the value of one part. 63 m is shared into 9 equal parts, so divide it by 9.63 m ÷ 9 = 7 m for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.4 parts: 4 × 7 m = 28 m
5 parts: 5 × 7 m = 35 m
Check. Add the shares: 28 m + 35 m = 63 m, which is the total 63 m. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.3 + 4 = 7 parts
- Find the value of one part. £84 is shared into 7 equal parts, so divide it by 7.£84 ÷ 7 = £12 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Amir: 3 × £12 = £36
Beth: 4 × £12 = £48
Check. Add the shares: £36 + £48 = £84, which is the total £84. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.1 + 2 + 3 = 6 parts
- Find the value of one part. £600 is shared into 6 equal parts, so divide it by 6.£600 ÷ 6 = £100 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Ana: 1 × £100 = £100
Ben: 2 × £100 = £200
Cat: 3 × £100 = £300
Check. Add the shares: £100 + £200 + £300 = £600, which is the total £600. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.1 + 2 + 3 = 6 parts
- Find the value of one part. 60 is shared into 6 equal parts, so divide it by 6.60 ÷ 6 = 10 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.1 part: 1 × 10 = 10
2 parts: 2 × 10 = 20
3 parts: 3 × 10 = 30
Check. Add the shares: 10 + 20 + 30 = 60, which is the total 60. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.2 + 3 + 5 = 10 parts
- Find the value of one part. £120 is shared into 10 equal parts, so divide it by 10.£120 ÷ 10 = £12 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.2 parts: 2 × £12 = £24
3 parts: 3 × £12 = £36
5 parts: 5 × £12 = £60
Check. Add the shares: £24 + £36 + £60 = £120, which is the total £120. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.3 + 4 + 8 = 15 parts
- Find the value of one part. 90 kg is shared into 15 equal parts, so divide it by 15.90 kg ÷ 15 = 6 kg for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.3 parts: 3 × 6 kg = 18 kg
4 parts: 4 × 6 kg = 24 kg
8 parts: 8 × 6 kg = 48 kg
Check. Add the shares: 18 kg + 24 kg + 48 kg = 90 kg, which is the total 90 kg. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.1 + 5 = 6 parts
- Find the value of one part. £2.40 is shared into 6 equal parts, so divide it by 6.£2.40 ÷ 6 = £0.40 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.1 part: 1 × £0.40 = £0.40
5 parts: 5 × £0.40 = £2
Check. Add the shares: £0.40 + £2 = £2.40, which is the total £2.40. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.2 + 3 = 5 parts
- Find the value of one part. £7.50 is shared into 5 equal parts, so divide it by 5.£7.50 ÷ 5 = £1.50 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Dan: 2 × £1.50 = £3
Eve: 3 × £1.50 = £4.50
Check. Add the shares: £3 + £4.50 = £7.50, which is the total £7.50. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.4 + 1 = 5 parts
- Find the value of one part. 20 kg is shared into 5 equal parts, so divide it by 5.20 kg ÷ 5 = 4 kg for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.sand: 4 × 4 kg = 16 kg
cement: 1 × 4 kg = 4 kg
Check. Add the shares: 16 kg + 4 kg = 20 kg, which is the total 20 kg. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. The ratio 2 : 7 compares red with the whole bag. Change it to red : other, then share 49.
- Find the number of parts that are not red. The whole is 7 parts and red is 2 of them.7 − 2 = 5 parts
- Write the ratio red : other. Both numbers are parts now.2 : 5
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.2 + 5 = 7 parts
- Find the value of one part. 49 is shared into 7 equal parts, so divide it by 7.49 ÷ 7 = 7 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Red counters: 2 × 7 = 14
Other counters: 5 × 7 = 35
Check. Red should be 27 of 49 = 49 ÷ 7 × 2 = 14. ✓
Watch out. 7 is the whole bag, so the other counters are 5 parts, not 7 parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.7 + 5 = 12 parts
- Find the value of one part. 840 is shared into 12 equal parts, so divide it by 12.840 ÷ 12 = 70 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Boys: 7 × 70 = 490
Girls: 5 × 70 = 350
Check. Add the shares: 490 + 350 = 840, which is the total 840. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.5 + 4 + 3 = 12 parts
- Find the value of one part. £2400 is shared into 12 equal parts, so divide it by 12.£2400 ÷ 12 = £200 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Partner 1: 5 × £200 = £1000
Partner 2: 4 × £200 = £800
Partner 3: 3 × £200 = £600
Check. Add the shares: £1000 + £800 + £600 = £2400, which is the total £2400. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Add the parts to find how many equal parts there are, find the value of one part, then multiply.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.4 + 3 = 7 parts
- Find the value of one part. £84 is shared into 7 equal parts, so divide it by 7.£84 ÷ 7 = £12 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Priya: 4 × £12 = £48
Sam: 3 × £12 = £36
Check. Add the shares: £48 + £36 = £84, which is the total £84. ✓
Watch out. Do not divide the total by one of the ratio numbers. Divide by the total number of parts.
Method. Work out the larger share in each competition, then compare.
- Competition A: one part. Total parts 2 + 3 = 5, and £60 ÷ 5 = £12.£60 ÷ 5 = £12
- Competition A: the larger share. The larger ratio number is 3.3 × £12 = £36
- Competition B: one part. Total parts 1 + 3 = 4, and £80 ÷ 4 = £20.£80 ÷ 4 = £20
- Competition B: the larger share. The larger ratio number is 3.3 × £20 = £60
- Compare. £60 is bigger than £36.Competition B has the bigger top prize: £60.
Check. Competition B total £80 > £60, and the larger share is 3 of 4 parts = 75% of £80 = £60. ✓
Watch out. A bigger ratio number does not always give a bigger share: the total matters too.
Method. Sophie has not found the value of one part. Dividing by one ratio number at a time gives amounts that do not add up to the total.
- Check Sophie's answers. £50 ÷ 2 = £25 and £50 ÷ 3 = £16.67 (to the nearest penny). These add to £41.67, not £50.25 + 16.67 = 41.67
- Explain the mistake. The ratio 2 : 3 splits the money into 2 + 3 = 5 equal parts. We must divide by the total number of parts.2 + 3 = 5 parts
- Find the value of one part. Divide the total by 5.£50 ÷ 5 = £10
- Work out the shares. Multiply by each ratio number.2 × £10 = £20 and 3 × £10 = £30
Check. £20 + £30 = £50. ✓
Watch out. Divide by the total number of parts, which you find by adding the ratio numbers.
Method. Work out the value of one part. If it is not a whole number, the shares will not be whole numbers of pounds (unless the ratio number cancels it).
- Add the parts. There are 3 + 4 parts.3 + 4 = 7 parts
- Find the value of one part. Divide £50 by 7.£50 ÷ 7 = £7.1429... (it does not divide exactly)
- Check the shares. The shares are 3 and 4 times this amount. Since 7 does not divide into 50 and 3 and 4 have no factor of 7, neither share is a whole number of pounds.3 × 50 ÷ 7 = 21.43... and 4 × 50 ÷ 7 = 28.57...
- Answer. No: the shares are not whole numbers because 50 is not a multiple of 7.
Check. A total that can be shared in a whole number of pounds in the ratio 3 : 4 must be a multiple of 7, for example £49 or £56. ✓
Watch out. The total must be a multiple of the sum of the ratio numbers for the shares to be whole numbers.
Key words. To share in a ratio means to split an amount into equal-sized parts, then give each person the number of parts shown in the ratio. The ratio 3 : 5 means 3 parts for the first person and 5 parts for the second.
Method. Find the three shares, then change Dad's and Ella's amounts, then simplify the new ratio.
- Add up the parts of the ratio. Each number in the ratio is a number of equal parts. The total number of parts is the sum of the ratio numbers.3 + 2 + 1 = 6 parts
- Find the value of one part. £240 is shared into 6 equal parts, so divide it by 6.£240 ÷ 6 = £40 for one part
- Multiply to find each share. Each person gets as many parts as their ratio number, so multiply the value of one part by that number.Mum: 3 × £40 = £120
Dad: 2 × £40 = £80
Ella: 1 × £40 = £40 - Dad gives half of his share to Ella. Half of Dad's £80 is £40. Take it from Dad and add it to Ella.Dad: £80 − £40 = £40
Ella: £40 + £40 = £80 - Write the new ratio. Mum has not changed.Mum : Dad : Ella = 120 : 40 : 80
- Simplify. Divide every part by the HCF, which is 40.120 ÷ 40 = 3, 40 ÷ 40 = 1, 80 ÷ 40 = 2, so 3 : 1 : 2
Check. The total is still 120 + 40 + 80 = £240. ✓
Watch out. The total does not change when money is given from one person to another.