Lesson 1: Understand Ratios

Property

A ratio is commonly described as a pair of positive numbers, written $a : b$ and read as “$a$ to $b$.” When describing a ratio, the order of the quantities must be the same as the order of the numbers.

Examples

• In a garden, there are 5 rose bushes for every 2 lilac bushes. The ratio of roses to lilacs is 5:2.
• A pancake recipe requires 2 cups of flour for every 1 cup of milk. The ratio of flour to milk is 2:1.
• For every 3 games the team wins, they lose 1. The ratio of wins to losses is 3:1.

Explanation

A ratio is a recipe for comparing two amounts. It tells you, "for every this, you have that." The order is critical—a ratio of 2:3 is not the same as 3:2, just like putting on shoes then socks doesn't work!

Property

The two numbers, $a$ and $b$, that form a ratio are called its terms. In a ratio comparing quantity A to quantity B, the first term corresponds to quantity A and the second term corresponds to quantity B.

Examples

Property

A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of $a$ to $b$ is written $a$ to $b$, $\frac{a}{b}$, or $a:b$.

Examples

• The ratio 20 to 36 can be written as $20\ \text{to}\ 36$, $20:36$, and $\frac{20}{36}$, which simplifies to $\frac{5}{9}$.

• The ratio 45 to 18 can be written as $45\ \text{to}\ 18$, $45:18$, and $\frac{45}{18}$, which simplifies to $\frac{5}{2}$.