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Sharing in a given ratio and scaling a recipe up or down.
Question 1 of 12
Freya and Harry share 42 conkers in the ratio 2:5. How many does the one with the larger share get?
A ratio of 2:5 means the conkers are split into 2 + 5 = 7 equal parts. 42 ÷ 7 = 6, so one part is 6 conkers. The larger share is 5 parts: 6 × 5 = 30. Checking the two shares add back to the total — 30 + 12 = 42 — is worth the few seconds. Always check the shares add back up to what you started with.
The answer is C. A ratio of 2:5 means the conkers are split into 2 + 5 = 7 equal parts. 42 ÷ 7 = 6, so one part is 6 conkers. The larger share is 5 parts: 6 × 5 = 30. Checking the two shares add back to the total — 30 + 12 = 42 — is worth the few seconds. Always check the shares add back up to what you started with.
A recipe for 4 people uses 150 g of grated cheese. How much grated cheese is needed for 12 people?
Find the amount for one person first: 150 g ÷ 4 = 37.5 g each. For 12 people that is 37.5 g × 12 = 450 g. The answer has to be larger than 150 g, because more people are being fed. If the number of people doubles, so does every ingredient. Spotting that saves the long method.
The answer is D. Find the amount for one person first: 150 g ÷ 4 = 37.5 g each. For 12 people that is 37.5 g × 12 = 450 g. The answer has to be larger than 150 g, because more people are being fed. If the number of people doubles, so does every ingredient. Spotting that saves the long method.
Omar and Dylan share 153 conkers in the ratio 4:5. How many does the one with the larger share get?
A ratio of 4:5 means the conkers are split into 4 + 5 = 9 equal parts. 153 ÷ 9 = 17, so one part is 17 conkers. The larger share is 5 parts: 17 × 5 = 85. Checking the two shares add back to the total — 85 + 68 = 153 — is worth the few seconds. Always check the shares add back up to what you started with.
The answer is C. A ratio of 4:5 means the conkers are split into 4 + 5 = 9 equal parts. 153 ÷ 9 = 17, so one part is 17 conkers. The larger share is 5 parts: 17 × 5 = 85. Checking the two shares add back to the total — 85 + 68 = 153 — is worth the few seconds. Always check the shares add back up to what you started with.
Tomasz and Rosie share 45 conkers in the ratio 5:4. How many does the one with the larger share get?
A ratio of 5:4 means the conkers are split into 5 + 4 = 9 equal parts. 45 ÷ 9 = 5, so one part is 5 conkers. The larger share is 5 parts: 5 × 5 = 25. Checking the two shares add back to the total — 25 + 20 = 45 — is worth the few seconds. Always check the shares add back up to what you started with.
The answer is A. A ratio of 5:4 means the conkers are split into 5 + 4 = 9 equal parts. 45 ÷ 9 = 5, so one part is 5 conkers. The larger share is 5 parts: 5 × 5 = 25. Checking the two shares add back to the total — 25 + 20 = 45 — is worth the few seconds. Always check the shares add back up to what you started with.
Zainab and Priya share 40 conkers in the ratio 2:3. How many does the one with the larger share get?
A ratio of 2:3 means the conkers are split into 2 + 3 = 5 equal parts. 40 ÷ 5 = 8, so one part is 8 conkers. The larger share is 3 parts: 8 × 3 = 24. Checking the two shares add back to the total — 24 + 16 = 40 — is worth the few seconds. Dividing by 2 only works when the ratio is 1:1. Read the ratio before assuming.
The answer is C. A ratio of 2:3 means the conkers are split into 2 + 3 = 5 equal parts. 40 ÷ 5 = 8, so one part is 8 conkers. The larger share is 3 parts: 8 × 3 = 24. Checking the two shares add back to the total — 24 + 16 = 40 — is worth the few seconds. Dividing by 2 only works when the ratio is 1:1. Read the ratio before assuming.
Alfie and Zainab share 98 conkers in the ratio 4:3. How many does the one with the larger share get?
A ratio of 4:3 means the conkers are split into 4 + 3 = 7 equal parts. 98 ÷ 7 = 14, so one part is 14 conkers. The larger share is 4 parts: 14 × 4 = 56. Checking the two shares add back to the total — 56 + 42 = 98 — is worth the few seconds. Always check the shares add back up to what you started with.
The answer is C. A ratio of 4:3 means the conkers are split into 4 + 3 = 7 equal parts. 98 ÷ 7 = 14, so one part is 14 conkers. The larger share is 4 parts: 14 × 4 = 56. Checking the two shares add back to the total — 56 + 42 = 98 — is worth the few seconds. Always check the shares add back up to what you started with.
A recipe for 6 people uses 75 g of grated cheese. How much grated cheese is needed for 12 people?
Find the amount for one person first: 75 g ÷ 6 = 12.5 g each. For 12 people that is 12.5 g × 12 = 150 g. The answer has to be larger than 75 g, because more people are being fed. If the number of people doubles, so does every ingredient. Spotting that saves the long method.
The answer is B. Find the amount for one person first: 75 g ÷ 6 = 12.5 g each. For 12 people that is 12.5 g × 12 = 150 g. The answer has to be larger than 75 g, because more people are being fed. If the number of people doubles, so does every ingredient. Spotting that saves the long method.
A recipe for 6 people uses 200 g of caster sugar. How much caster sugar is needed for 18 people?
Find the amount for one person first: 200 g ÷ 6 = 33.333 g each. For 18 people that is 33.333 g × 18 = 600 g. The answer has to be larger than 200 g, because more people are being fed. Work out the amount for one, then scale up. It works whatever the numbers are, even when they do not divide neatly.
The answer is A. Find the amount for one person first: 200 g ÷ 6 = 33.333 g each. For 18 people that is 33.333 g × 18 = 600 g. The answer has to be larger than 200 g, because more people are being fed. Work out the amount for one, then scale up. It works whatever the numbers are, even when they do not divide neatly.
A recipe for 4 people uses 75 g of grated cheese. How much grated cheese is needed for 8 people?
Find the amount for one person first: 75 g ÷ 4 = 18.75 g each. For 8 people that is 18.75 g × 8 = 150 g. The answer has to be larger than 75 g, because more people are being fed. Work out the amount for one, then scale up. It works whatever the numbers are, even when they do not divide neatly.
The answer is A. Find the amount for one person first: 75 g ÷ 4 = 18.75 g each. For 8 people that is 18.75 g × 8 = 150 g. The answer has to be larger than 75 g, because more people are being fed. Work out the amount for one, then scale up. It works whatever the numbers are, even when they do not divide neatly.
A recipe for 8 people uses 100 g of sultanas. How much sultanas is needed for 24 people?
Find the amount for one person first: 100 g ÷ 8 = 12.5 g each. For 24 people that is 12.5 g × 24 = 300 g. The answer has to be larger than 100 g, because more people are being fed. If the number of people doubles, so does every ingredient. Spotting that saves the long method.
The answer is D. Find the amount for one person first: 100 g ÷ 8 = 12.5 g each. For 24 people that is 12.5 g × 24 = 300 g. The answer has to be larger than 100 g, because more people are being fed. If the number of people doubles, so does every ingredient. Spotting that saves the long method.
Ivy and Isla share 168 conkers in the ratio 4:3. How many does the one with the larger share get?
A ratio of 4:3 means the conkers are split into 4 + 3 = 7 equal parts. 168 ÷ 7 = 24, so one part is 24 conkers. The larger share is 4 parts: 24 × 4 = 96. Checking the two shares add back to the total — 96 + 72 = 168 — is worth the few seconds. Dividing by 2 only works when the ratio is 1:1. Read the ratio before assuming.
The answer is C. A ratio of 4:3 means the conkers are split into 4 + 3 = 7 equal parts. 168 ÷ 7 = 24, so one part is 24 conkers. The larger share is 4 parts: 24 × 4 = 96. Checking the two shares add back to the total — 96 + 72 = 168 — is worth the few seconds. Dividing by 2 only works when the ratio is 1:1. Read the ratio before assuming.
A recipe for 4 people uses 200 g of grated cheese. How much grated cheese is needed for 8 people?
Find the amount for one person first: 200 g ÷ 4 = 50 g each. For 8 people that is 50 g × 8 = 400 g. The answer has to be larger than 200 g, because more people are being fed. Work out the amount for one, then scale up. It works whatever the numbers are, even when they do not divide neatly.
The answer is B. Find the amount for one person first: 200 g ÷ 4 = 50 g each. For 8 people that is 50 g × 8 = 400 g. The answer has to be larger than 200 g, because more people are being fed. Work out the amount for one, then scale up. It works whatever the numbers are, even when they do not divide neatly.
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