Ratio

A ratio compares two or more quantities by division. The ratio $a : b$ means $a$ divided by $b$, or $\frac{a}{b}$. Ratios can involve more than two numbers, such as $a : b : c$. Ratios can be scaled up or down by multiplying or dividing all parts by the same nonzero number, which does not change the relationship.

Important properties

• Ratios can be simplified by dividing all terms by their greatest common divisor.

• Ratios can be written as fractions: $a : b$ is the same as $\frac{a}{b}$.

• Equivalent ratios represent the same relationship (e.g., $2 : 3$ and $4 : 6$).

• Ratios can be used to solve problems involving proportions, mixtures, and scaling.