Maths
What is a ratio?
Quick answer
A ratio compares two or more amounts, written with a colon. A ratio of 2:3 means for every 2 of one thing there are 3 of the other.
In one sentence
A ratio tells you how much of one thing there is compared with another.
Explained
Picture a jug of lemonade made from 1 cup of lemon juice and 4 cups of water. The ratio of juice to water is 1 to 4, written 1:4. Make a bigger jug with 2 cups of juice and 8 cups of water, and it tastes exactly the same, because the ratio 2:8 is the same as 1:4.
lemon
juice
cup- cup
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Order matters. "Juice to water is 1:4" is not the same as "water to juice is 1:4". Always check which amount comes first.
You simplify a ratio just like a fraction: divide every part by the same number. 10:15 becomes 2:3 (divide by 5). 18:24:30 becomes 3:4:5 (divide by 6). Scaling up works the same way with multiplication.
Ratios and fractions are related but not identical. If cats and dogs at a shelter are in the ratio 3:2, there are 3 + 2 = 5 parts altogether. So ⅗ of the animals are cats and ⅖ are dogs. The fraction compares a part with the whole; the ratio compares a part with another part.
Sharing in a ratio is a classic problem. To share 40 sweets between Kemi and Tom in the ratio 3:5, add the parts (3 + 5 = 8), find one part (40 ÷ 8 = 5), then multiply: Kemi gets 3 × 5 = 15 and Tom gets 5 × 5 = 25. Check: 15 + 25 = 40.
Examples
| Situation | Ratio |
|---|---|
| 6 apples to 9 oranges | 6:9 = 2:3 |
| Map scale, 1 cm to 1 km | 1:100 000 |
| Recipe: 200 g flour to 100 g butter | 2:1 |
| Share 60 in 1:2:3 | 10, 20 and 30 |
Worked example: a recipe for 4 people uses 300 g of rice. For 6 people, scale by 6 ÷ 4 = 1.5, so use 450 g.
Common mistakes
- Swapping the order, writing boys:girls when asked for girls:boys. Fix: write the labels above the numbers.
- Dividing by the wrong total. Sharing in 3:5 means dividing by 8, not by 3 or 5.
- Adding instead of multiplying to scale: 2:3 is not the same as 4:5. Fix: multiply both parts by the same number, giving 4:6.
Quick quiz
Ratio
Check what you know with 4 quick questions.
Question 1 of 4
A class has 12 girls and 15 boys. What is the ratio of girls to boys in its simplest form?
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Related topics
Fractions
A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.
Percentages
A percentage is a number out of 100, written with the sign %. So 25% means 25 out of every 100, which is the same as one quarter.
Multiplication
Multiplication is adding equal groups quickly. 4 × 3 means 4 groups of 3 (or 3 groups of 4), which makes 12. The answer is called the product.
Division
Division is sharing into equal groups, or finding how many groups fit. The sign is ÷, so 12 ÷ 3 = 4. The answer is called the quotient.
Direct proportion
Two quantities are in direct proportion when one is always the same multiple of the other, so doubling one doubles the other. The rule is y = kx, where k is the constant of proportionality.
Profit and loss
Profit = selling price − cost price; loss = cost price − selling price. Profit percentage = profit ÷ cost price × 100. Buy at $20, sell at $25: profit $5, which is 25%.