Lesson 1: 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

Part to part ratio: Compares different parts of a larger group. For example, comparing the number of boys to the number of girls on a playground.

Part to total ratio (or part to whole ratio): Compares one part of a group to the entire group. For example, comparing the number of boys to the total number of children.

Total to part ratio: Compares the entire group to one of its parts. For example, comparing the total number of children to the number of girls.