4.1 Ratios

A ratio compares two quantities of the same kind by division. If a class has 12 boys and 18 girls, the ratio of boys to girls is \(12:18\), which is the same as \(2:3\), because a ratio is unchanged when both terms are multiplied or divided by the same non-zero number. A ratio therefore records only the relative sizes of the quantities, not their actual values, and the first step in almost every problem is to restore the scale by introducing a common multiplier. If