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

A part-to-part ratio compares the sizes of different parts of a given population. For example, the ratio of right-handed people to left-handed people.
A part-to-whole ratio compares one part of a population to the entire population. For example, saying “one in ten people is left-handed” is a part-to-whole ratio.

Examples

• In a fruit basket with 5 apples and 8 bananas, the part-to-part ratio of apples to bananas is $5:8$. The part-to-whole ratio of apples to all fruit is $5:13$.
• A classroom has 12 girls and 15 boys. The part-to-part ratio of girls to boys is $12:15$, which simplifies to $4:5$. The part-to-whole ratio of boys to students is $15:27$, which simplifies to $5:9$.
• A bag contains 10 red marbles and 6 blue marbles. The part-to-part ratio of blue to red is $6:10$. The part-to-whole ratio of blue to all marbles is $6:16$.

Explanation

Think of it like a pizza! A part-to-part ratio compares pepperoni slices to mushroom slices. A part-to-whole ratio compares pepperoni slices to the total number of slices in the whole pizza.