Ratio

A ratio is a way of showing how two numbers or quantities relate to each other. It is usually written as a : b, or as a fraction a/b. For example, if a group contains 8 girls and 4 boys, the ratio of girls to boys is 8 : 4, which can be simplified to 2 : 1.

A ratio shows a comparative relationship and is not an absolute count. The ratio 2 : 1 is equivalent to 4 : 2 and 100 : 50, because both parts have been multiplied or divided by the same number. For this reason, every ratio has a simplified form, which is the one where the two numbers share no common divisor greater than one.

Notation and measurement

A ratio can be written in three equivalent ways: as a proportion (a : b), as a fraction (a/b), or as a decimal such as 0.5. When the two quantities are the same type—for example, length and length—the ratio is dimensionless. When the types are different, such as distance and time, the result is a rate (such as speed), not a simple ratio.

A ratio can also involve more than two parts, for example 2 : 3 : 5. This form is used to divide something into several parts, such as dividing money or sharing ingredients in a mixture.

Proportion

When two ratios are equal—such as a : b = c : d—this is called a proportion. In that case, it is true that a×d = b×c, known as cross-multiplication. This method is used to find an unknown number when the other three are known.

Uses

Ratios are applied in many fields: maps (map scales), architecture and technical drawings, recipe formulation and pharmaceuticals, and financial calculations such as interest rates and asset ratios. Percentages are a form of ratio based on 100, for example 25% is equivalent to 25 : 100 or 1 : 4.