Year 6: Unequal sharing
Part of the Year 6 ratio and proportion chapter. Chapter overview · whole chapter on one page
Unequal sharing
Sometimes a total is shared into unequal amounts, in a given ratio. Follow four steps. 1 Add the numbers in the ratio to find the total number of parts. 2 Divide the total by this number to find the value of one part. 3 Multiply each number in the ratio by the value of one part. 4 Check that the shares add up to the total.
A share can also be written as a fraction of the total. In the ratio 2:3 the first share is 2 of the 5 parts, which is 2/5 of the total. The multiples of the ratio numbers help us to find the value of one part quickly.
Key ideas
- The number of parts is the total of the numbers in the ratio.
- One part = total ÷ number of parts.
- Each share = its number in the ratio × the value of one part.
- The shares must add up to the total. Check every time.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 45 into 5 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.2 + 3 = 5 parts
- Divide the total by 5 to find the value of one part. Every part is the same size.45 ÷ 5 = 9
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.2 × 9 = 18; 3 × 9 = 27
- Check: the shares add up to the total. If they do not, check the working.18 + 27 = 45
- Write the share that the question asks for: Ben. Ben gets 27.27
Check. The ratio of the shares is 2:3, and they add up to 45. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 60 into 5 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.1 + 4 = 5 parts
- Divide the total by 5 to find the value of one part. Every part is the same size.60 ÷ 5 = 12
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.1 × 12 = 12; 4 × 12 = 48
- Check: the shares add up to the total. If they do not, check the working.12 + 48 = 60
- Write the share that the question asks for: Big share. Big share gets 48.48
Check. The ratio of the shares is 1:4, and they add up to 60. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 120 into 10 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.2 + 3 + 5 = 10 parts
- Divide the total by 10 to find the value of one part. Every part is the same size.120 ÷ 10 = 12
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.2 × 12 = 24; 3 × 12 = 36; 5 × 12 = 60
- Check: the shares add up to the total. If they do not, check the working.24 + 36 + 60 = 120
- Write the share that the question asks for: Third friend. Third friend gets 60.60
Check. The ratio of the shares is 2:3:5, and they add up to 120. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Watch out
Do not share the total equally. 45 ÷ 2 is not the answer when the ratio is 2:3. Find the number of parts first.
Exam tip
Grown-up tip. Ask: “How many equal parts are there altogether?” Then: “How much is one part?” Finally: “Do the shares add up to the total?”
Exercise 7E Unequal sharing
Non-calculatorKey words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 24 into 3 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.1 + 2 = 3 parts
- Divide the total by 3 to find the value of one part. Every part is the same size.24 ÷ 3 = 8
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.1 × 8 = 8; 2 × 8 = 16
- Check: the shares add up to the total. If they do not, check the working.8 + 16 = 24
- Write the share that the question asks for: Smaller. Smaller gets 8.8
Check. The ratio of the shares is 1:2, and they add up to 24. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 24 into 3 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.1 + 2 = 3 parts
- Divide the total by 3 to find the value of one part. Every part is the same size.24 ÷ 3 = 8
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.1 × 8 = 8; 2 × 8 = 16
- Check: the shares add up to the total. If they do not, check the working.8 + 16 = 24
- Write the share that the question asks for: Bigger. Bigger gets 16.16
Check. The ratio of the shares is 1:2, and they add up to 24. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 40 into 8 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.3 + 5 = 8 parts
- Divide the total by 8 to find the value of one part. Every part is the same size.40 ÷ 8 = 5
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.3 × 5 = 15; 5 × 5 = 25
- Check: the shares add up to the total. If they do not, check the working.15 + 25 = 40
- Write the share that the question asks for: Second. Second gets 25.25
Check. The ratio of the shares is 3:5, and they add up to 40. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 90 into 9 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.4 + 5 = 9 parts
- Divide the total by 9 to find the value of one part. Every part is the same size.90 ÷ 9 = 10
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.4 × 10 = 40; 5 × 10 = 50
- Check: the shares add up to the total. If they do not, check the working.40 + 50 = 90
- Write the share that the question asks for: Ben. Ben gets 50.50
Check. The ratio of the shares is 4:5, and they add up to 90. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 72 into 8 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.1 + 3 + 4 = 8 parts
- Divide the total by 8 to find the value of one part. Every part is the same size.72 ÷ 8 = 9
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.1 × 9 = 9; 3 × 9 = 27; 4 × 9 = 36
- Check: the shares add up to the total. If they do not, check the working.9 + 27 + 36 = 72
- Write the share that the question asks for: First. First gets 9.9
Check. The ratio of the shares is 1:3:4, and they add up to 72. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 72 into 8 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.1 + 3 + 4 = 8 parts
- Divide the total by 8 to find the value of one part. Every part is the same size.72 ÷ 8 = 9
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.1 × 9 = 9; 3 × 9 = 27; 4 × 9 = 36
- Check: the shares add up to the total. If they do not, check the working.9 + 27 + 36 = 72
- Write the share that the question asks for: Third. Third gets 36.36
Check. The ratio of the shares is 1:3:4, and they add up to 72. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 36 into 9 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.5 + 4 = 9 parts
- Divide the total by 9 to find the value of one part. Every part is the same size.36 ÷ 9 = 4
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.5 × 4 = 20; 4 × 4 = 16
- Check: the shares add up to the total. If they do not, check the working.20 + 16 = 36
- Write the share that the question asks for: Ava. Ava gets 20.20
Check. The ratio of the shares is 5:4, and they add up to 36. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 15 into 5 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.2 + 3 = 5 parts
- Divide the total by 5 to find the value of one part. Every part is the same size.15 ÷ 5 = 3
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.2 × 3 = 6; 3 × 3 = 9
- Check: the shares add up to the total. If they do not, check the working.6 + 9 = 15
- Write the share that the question asks for: white. white gets 9.9
Check. The ratio of the shares is 2:3, and they add up to 15. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Find the value of one part from the known share, then find the amount asked for.
- Find the value of one part: 14 ÷ 2. The known share is some number of parts.14 ÷ 2 = 7
- Find Ben. Ben has 5 parts.7 × 5 = 35
- Write the answer. 35
Check. 2 parts is 14, so one part is 7. ✓
Watch out. Find the value of one part first, then multiply. Do not divide the total by 2.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Find the value of one part from the known share, then find the amount asked for.
- Find the value of one part: 14 ÷ 2. The known share is some number of parts.14 ÷ 2 = 7
- Find the total. The ratio has 7 parts altogether.7 × 7 = 49
- Write the answer. 49
Check. 2 parts is 14, so one part is 7. ✓
Watch out. Find the value of one part first, then multiply. Do not divide the total by 2.
Key words. A ratio is made of parts. Every part is the same size. The total is all the parts added together.
Method. Find the total parts, then the fraction that Sam has.
- Add the parts of the ratio: 1 + 2. The total number of parts is 3.1 + 2 = 3 parts
- Sam has 2 of the 3 parts. So Sam has 2 out of 3 equal parts of the money.2 parts out of 3
- Write the answer as a fraction. The fraction is the parts Sam has over the total parts.2/3
Check. 1/3 + 2/3 = 3/3, which is the whole amount. ✓
Watch out. The fraction uses the parts of the ratio, not the money. Sam has the bigger share, so the fraction is bigger than 1/2.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 50 into 5 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.2 + 3 = 5 parts
- Divide the total by 5 to find the value of one part. Every part is the same size.50 ÷ 5 = 10
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.2 × 10 = 20; 3 × 10 = 30
- Check: the shares add up to the total. If they do not, check the working.20 + 30 = 50
- Write the share that the question asks for: Big share. Big share gets 30.30
Check. The ratio of the shares is 2:3, and they add up to 50. ✓
Watch out. Find the value of one part first. Do not share the total equally.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Check the shares: they must be in the ratio 1:2 and add up to 36.
- Find the total parts: 1 + 2 = 3. Each share is a number of these parts.1 + 2 = 3 parts
- Find one part: 36 ÷ 3. One part is the total divided by the number of parts.36 ÷ 3 = 12
- Find the two shares: 1 × 12 and 2 × 12. Each share is its number of parts.1 × 12 = 12, and 2 × 12 = 24
- Write the answer. The shares add up to 36, so Sam is right.Yes. 12 and 24 are in the ratio 1:2, and 12 + 24 = 36.
Check. 12 + 24 = 36, and 24 ÷ 12 = 2. ✓
Watch out. Check that the shares add up to the total before you agree.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Add the parts, then check whether 50 divides exactly into that number of parts.
- Add the parts: 2 + 3 + 4. The total number of parts is 9.2 + 3 + 4 = 9 parts
- Divide 50 by 9. For the shares to be whole numbers, 9 must divide exactly into 50.50 ÷ 9 = 5 remainder 5
- Write the answer. There is a remainder, so the shares are not whole numbers.No. 50 is not a multiple of 9.
Check. 9 × 5 = 45, and 50 - 45 = 5 is left over. ✓
Watch out. The total must be a multiple of the number of parts.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Find the difference in parts, then the value of one part, then the total.
- Find the difference in parts: 7 − 3 = 4. Ben has 4 more parts than Adam.7 − 3 = 4 parts
- Find one part: 36 ÷ 4. The difference of £36 is 4 parts.36 ÷ 4 = 9
- Find the total number of parts: 3 + 7 = 10. The total is made of 10 parts.3 + 7 = 10 parts
- Find the total money: 10 × 9. Each part is £9.10 × 9 = 90
- Write the answer. 90
Check. Adam has 3 × 9 = 27 and Ben has 7 × 9 = 63. 63 - 27 = 36, and 27 + 63 = 90. ✓
Watch out. The difference is in parts, not in pounds. Find one part first.
Key words. To share in a ratio means to split a total into shares that have the same ratio as the numbers given.
Method. Share 48 into 12 equal parts, then give each share its number of parts.
- Add the parts of the ratio to find the total number of parts. Each number in the ratio counts equal parts.5 + 7 = 12 parts
- Divide the total by 12 to find the value of one part. Every part is the same size.48 ÷ 12 = 4
- Multiply each number in the ratio by the value of one part. Each share is its number of parts.5 × 4 = 20; 7 × 4 = 28
- Check: the shares add up to the total. If they do not, check the working.20 + 28 = 48
- Write the share that the question asks for: Max. Max gets 28.28
Check. The ratio of the shares is 5:7, and they add up to 48. ✓
Watch out. Find the value of one part first. Do not share the total equally.