How it works
A ratio of 7 : 3 means for every 7 of the first thing there are 3 of the second. Together that is 7 + 3 = 10 parts.
Sharing a total: divide the total by the number of parts to get one part, then multiply. With 40 students in a 7 : 3 ratio, one part is 40 ÷ 10 = 4, so there are 28 and 12.
Scaling: a ratio stays the same when you multiply both sides by the same number. If 3 zips = 6 squawks, then 27 zips (9 times as many) = 54 squawks. Write ratios as fractions when you need to set up a proportion and cross-multiply.
Ratios practice problems with solutions
These problems come from Mathyessy's question bank. Try each one before opening the solution.
The ratio of boys to girls is 7:3. If there are 40 students, how many are girls?
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Answer: 12
There are 7 + 3 = 10 parts, so one part is 40 ÷ 10 = 4. Girls: 3 × 4 = 12.
Two numbers are in the ratio 9:8 and sum to 51. What is the smaller?
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Answer: 24
9 + 8 = 17 parts, so one part is 51 ÷ 17 = 3. The smaller is 8 × 3 = 24.
If 3 zips equal 6 squawks, how many squawks equal 27 zips?
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Answer: 54
27 zips is 9 times 3 zips, so it equals 9 × 6 = 54 squawks. (Each zip is 2 squawks.)
If 4 zips equal 6 squawks, how many squawks equal 16 zips?
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Answer: 24
16 zips is 4 times 4 zips, so it equals 4 × 6 = 24 squawks.
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