Proportion: worked example
| a | 3 |
|---|---|
| b | 4 |
| c | 15 |
| Unknown value (x) | 20 |
| First ratio as a decimal | 0.75 |
Proportion: formula
Enter three of the four terms of a proportion a over b equals c over x, and the calculator solves for the unknown x. Make sure the terms line up: a and c should be the same kind of quantity, and b and x should be the same kind. For example, if 3 cups make 4 servings, then 15 cups make how many servings: a is 3, b is 4 and c is 15.
Use the same units on matching terms.
Proportion: changing a
| a | Unknown value (x) | First ratio as a decimal |
|---|---|---|
| 1 | 60 | 0.25 |
| 2 | 30 | 0.5 |
| 3 (example) | 20 | 0.75 |
| 4 | 15 | 1 |
| 5 | 12 | 1.3 |
Proportion: compare input ranges
| Input | Tested from | To | Unknown value (x): low input | Unknown value (x): high input | Swing |
|---|---|---|---|---|---|
| a | 2 | 4 | 30 | 15 | 15 (75%) |
| b | 3 | 5 | 15 | 25 | 10 (50%) |
| c | 14 | 17 | 18.7 | 22.7 | 4 (20%) |
Proportion: individual input comparisons
| Input | Value | Unknown value (x) | First ratio as a decimal |
|---|---|---|---|
| a | 1 | 60 | 0.25 |
| 2 | 30 | 0.5 | |
| 3 | 20 | 0.75 | |
| 4 | 15 | 1 | |
| 5 | 12 | 1.3 | |
| b | 2 | 10 | 1.5 |
| 3 | 15 | 1 | |
| 4 | 20 | 0.75 | |
| 5 | 25 | 0.6 | |
| 6 | 30 | 0.5 | |
| c | 12 | 16 | 0.75 |
| 14 | 18.7 | 0.75 | |
| 15 | 20 | 0.75 | |
| 17 | 22.7 | 0.75 | |
| 18 | 24 | 0.75 |
Proportion: combined input changes
| a / b | 2 | 4 | 6 |
|---|---|---|---|
| 1 | 30 | 60 | 90 |
| 2 | 15 | 30 | 45 |
| 3 | 10 | 20 | 30 |
| 4 | 7.5 | 15 | 22.5 |
| 5 | 6 | 12 | 18 |
Proportion: which assumptions move the result?
Proportion: values and definitions
| Quantity and definition | Value used |
|---|---|
| a — The known top number of the first ratio. | 3 |
| b — The known bottom number of the first ratio. | 4 |
| c — The known top number of the second ratio. | 15 |
| Unknown value (x) | 20 |
| First ratio as a decimal | 0.75 |
Proportion: half and double a
| a | Unknown value (x) |
|---|---|
| 1.5 | 40 |
| 3 | 20 |
| 6 | 10 |
Common error: Putting one ratio upside down. Writing 3 over 4 equals x over 15 solves a different problem and returns 11.25 instead of 20.
Proportions assume a constant ratio, which does not hold for every situation: doubling the cooking time does not double the cooking quality, and fixed fees break proportionality. Inverse proportions, where one quantity rises as the other falls, need a different setup. If any term is zero, the result may be undefined.
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A proportion says two ratios are equal, and cross-multiplying finds the missing part. If 3 parts of concentrate go with 4 of water, then 15 parts of concentrate go with 20 of water. The same step scales a map distance, a recipe, a photo enlargement or a dose.
It works because both ratios describe the same relationship at different sizes.
Line up the units before you multiply. The top numbers must describe the same thing, and so must the bottom numbers.
Simplify ratios on the ratio simplifier calculator, and compute percentages on the percentage page. The unit price comparison and unit conversion calculators use proportions, and the fraction calculator handles the arithmetic. The percent difference page compares two values without a scale.
How do I solve a proportion?
Cross-multiply and divide: for a over b equal to c over x, x equals b times c divided by a.
What is the difference between direct and inverse proportion?
In direct proportion both quantities rise together at a constant ratio, and in inverse proportion one rises as the other falls so their product stays constant.
Where are proportions used in everyday life?
In recipes, map scales, currency conversion, dosing and pricing, whenever a rate is scaled up or down.