Ratio Calculator: Solve Proportions and Simplify Ratios
To solve a proportion, cross-multiply. In 3 : 4 = 15 : x, 3 × x = 4 × 15, so x = 60 ÷ 3 = 20. To simplify a ratio, divide every term by their greatest common divisor: 24 : 36 ÷ 12 = 2 : 3.
=
Leave exactly one box empty to solve for it.
D =
20 (3 : 4 = 15 : 20)
Show the math
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Cross-multiply
3 : 4 = 15 : D → 3 × D = 4 × 15
In a proportion the two ratios are equal, so the outer terms multiply to the same as the inner terms.
Read the steps as text
- Cross-multiply. 3 : 4 = 15 : D → 3 × D = 4 × 15 In a proportion the two ratios are equal, so the outer terms multiply to the same as the inner terms.
- Solve for D. D = B × C ÷ A = 4 × 15 ÷ 3 = 20
- Check: both ratios scale by the same factor. (3 : 4) × 5 = 15 : 20 Multiplying both terms of the first ratio by the same number gives the second.
Solving proportions
A proportion says two ratios are equal, A : B = C : D. Equal ratios have equal cross products, so A × D = B × C. If one term is missing, rearrange to find it: for D, that's D = B × C ÷ A. In 3 : 4 = 15 : x, x = 4 × 15 ÷ 3 = 20.
Proportions turn up everywhere: scaling a recipe from 4 servings to 10, working out a map distance from its scale, mixing paint or concrete in the right parts, or resizing an image without stretching it.
Simplifying ratios
A ratio is in its simplest form when its terms are whole numbers with no common factor other than 1. Find the greatest common divisor (GCD) of all the terms and divide each by it: the GCD of 24 and 36 is 12, so 24 : 36 simplifies to 2 : 3.
If a ratio has decimals, first multiply every term by the same power of ten to make them whole: 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5. The calculator also handles three or more terms, like 12 : 18 : 30 = 2 : 3 : 5.
Frequently asked questions
- How do I solve a ratio with a missing number?
- Cross-multiply and divide. For 2 : 5 = x : 20, x = 2 × 20 ÷ 5 = 8.
- How do I simplify a ratio?
- Divide all the terms by their greatest common divisor. 18 : 24 has a GCD of 6, so it simplifies to 3 : 4.
- How do I scale a recipe with ratios?
- Set up a proportion between the old and new amounts. If 4 servings need 300 g of flour, 10 servings need 300 × 10 ÷ 4 = 750 g. Enter 4 : 300 = 10 : x above.
- Is a ratio the same as a fraction?
- Closely related. The ratio 3 : 4 compares two quantities, while the fraction 3/4 is a part of a whole. A 3 : 4 ratio of boys to girls means boys are 3/7 of the group, not 3/4.