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Ratio and proportion calculator

  

A direct proportion: both ratios describe the same rate.

What do you want?

3 : 5 = 12 : x

20

x = 5 × 12 ÷ 3

How we got this

  1. Write it as fractions: 3/5 = 12/x.
  2. Cross-multiply: 3 × x = 5 × 12 = 60.
  3. Divide by 3: x = 20.

Ratios in practice

A proportion says two ratios are equal. Write each as a fraction and cross-multiply, which turns it into a one-step equation. The same move scales a recipe, reads a map scale or converts a currency at a fixed rate.

A ratio is a fraction, so the fraction calculator shows the same simplifying step. To turn a part of a ratio into a share, divide it by the total and use the percentage calculator.

Sources

What this calculator does not account for

  • Units: both sides must use the same units.
  • Rounding when the answer is not a whole number.

How this is calculated

Formula: Cross-multiplication

A : B =C : x ⇒ x =B × C ÷ A

What the symbols mean

  • A, B, CThe three known terms.

Good to know

  • To simplify a ratio, divide both parts by their greatest common divisor. Clear decimals first by multiplying both parts by 10, 100 and so on.

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Worked examples

Each example is worked out by the same code as the calculator above.

Recipe

3 cups of flour for 5 people. For 12: 3 : 5 = x : 12, so x = 3 × 12 ÷ 5 = 7.2 cups.

Simplify 1.5 : 2.5

× 10 = 15 : 25. GCD 5: 3 : 5.

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Questions

How do I solve 3:5 = 12:x?

Cross-multiply: 3x = 60, so x = 20.

How do I simplify 18:24?

The GCD is 6, so 18:24 = 3:4.

What is an inverse proportion?

When one goes up the other goes down, such as workers and days. Then A × B = C × x, so x = A × B ÷ C.