Unequal sharing and grouping
Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
What a learner can do afterwards
- Share 40 sweets between two children in the ratio 3:5
- Solve: 'Tom gets twice as many as Sam and Sam gets three times as many as Jo. If there are 30 altogether, how many does each get?'
- Use fraction knowledge to explain why sharing in ratio 2:3 means one person gets 2/5 of the total
1 · Read
A ratio like 3:5 shares an amount into equal parts. Add the two numbers to find how many parts there are altogether: 3 + 5 = 8. Every part is the same size, so nobody's part is bigger than anybody else's, they just hold different numbers of parts.
Each person's share is a fraction of the total parts. In a ratio of 2:3, the total is 2 + 3 = 5 parts, so one person gets 2/5 and the other gets 3/5. The ratio numbers go on top, and their sum always goes on the bottom. The two fractions add up to 5/5, the whole amount.
Sara and Ben share 40 sweets in the ratio 3:5. Total parts: 3 + 5 = 8. One part is 40 divided by 8, which is 5 sweets. Sara has 3 parts, so she gets 3 times 5, which is 15 sweets: that's 3/8 of the bag. Ben has 5 parts, so he gets 5 times 5, which is 25 sweets: that's 5/8 of the bag.
Tom, Sam and Jo share 30 sweets. Tom gets twice as many as Sam, and Sam gets three times as many as Jo. That makes the ratio Jo to Sam to Tom equal to 1:3:6. Total parts: 1 + 3 + 6 = 10. One part is 30 divided by 10, which is 3 sweets. So Jo gets 3, Sam gets 9, and Tom gets 18.
Before you share anything, add the ratio numbers first. That sum becomes the bottom number of every fraction share.
A ratio's numbers add up to the total parts, and each person's share is that number written as a fraction over the total.
2 · Watch
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Where this leads
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