Ratio Formulas

A ratio a : b compares two quantities by division.

Key formulas

simplest form: a : b = a÷g : b÷g, g = GCF(a, b)

share of A = total × a ÷ (a + b)

A as a fraction of the whole = a ÷ (a + b)

scaling: a : b = ka : kb for any k ≠ 0

Example

Split 84 in the ratio 3 : 4

  1. Parts: 3 + 4 = 7
  2. One part: 84 ÷ 7 = 12

36 and 48.

Ratio vs fraction

The ratio 3 : 4 compares part to part. The matching fractions compare part to whole: 3/7 and 4/7. Mixing these up is the most common ratio error — a 3 : 4 ratio of boys to girls does not mean 3/4 of the class are boys.