Percentages, Ratios & Proportions: A Practical Guide

Percentages express a quantity relative to 100. Ratios compare quantities, while proportions tell us when two ratios are equivalent.

Finding a percentage of a value

To find r% of a value V, use (r / 100) × V. For example, 15% of 240 is 0.15 × 240 = 36.

Percentage increase

If a value changes from an old value to a new value, percentage change is ((new − old) / old) × 100%. A positive answer indicates an increase; a negative answer indicates a decrease.

Ratios

A ratio such as 2:3 says that for every 2 units of the first quantity there are 3 units of the second. Ratios can be simplified by dividing both terms by their greatest common divisor.

Proportions

If a/b = c/d, cross multiplication gives ad = bc. This is useful for scaling recipes, converting quantities and solving many word problems.