Lesson 5: Part-part-whole Ratios

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.

Property

Part-to-part ratios compare individual parts: $a:b$

Part-to-whole ratios compare one part to the total: $a:(a+b)$ or $b:(a+b)$

Property

A tape diagram models division by showing a total amount (the dividend) broken into a number of equal parts (the divisor). The value of one part is the quotient.

Examples