Types of Ratios: Part-to-Part and Part-to-Whole
Types of ratios — part-to-part and part-to-whole — is a Grade 6 math concept in Reveal Math, Course 1. A part-to-part ratio compares one part of a group to another part: for example, 3 boys to 5 girls in a class (3:5). A part-to-whole ratio compares one part to the entire group: for example, 3 boys out of 8 total students (3:8). Both types are useful, but they answer different questions. Fractions and percents are always part-to-whole; understanding this distinction prevents confusion when setting up ratio problems.
Key Concepts
A ratio is a relationship that compares two quantities. Ratios can describe different types of relationships within a group: Part to Part Ratio: Compares one part of a group to another part of the same group. Part to Whole Ratio: Compares one part of a group to the entire group (the total).
Common Questions
What is a part-to-part ratio?
A part-to-part ratio compares one category within a group to another category in the same group. For example, if a bag has 4 red marbles and 6 blue marbles, the part-to-part ratio of red to blue is 4:6 or 2:3.
What is a part-to-whole ratio?
A part-to-whole ratio compares one part to the total (the whole group). For the same bag: the ratio of red marbles to total marbles is 4:10 or 2:5. This type of ratio is equivalent to a fraction.
How do you identify whether a ratio is part-to-part or part-to-whole?
Ask: is the comparison between two different categories (part-to-part), or between one category and the total (part-to-whole)? Look for the word total or the whole group being referenced to identify part-to-whole.
How are fractions and percents related to part-to-whole ratios?
Every fraction is a part-to-whole ratio — the numerator is the part and the denominator is the whole. Percents are part-to-whole ratios with 100 as the whole. Part-to-part ratios cannot be directly converted to fractions without first finding the total.
Can you convert a part-to-part ratio to a part-to-whole ratio?
Yes, if you know both parts. Find the total (sum of both parts), then create a part-to-whole ratio. For 3 cats to 5 dogs: total = 8 pets; part-to-whole for cats is 3:8.
When do students learn part-to-part and part-to-whole ratios?
These ratio types are introduced in Grade 6 in Reveal Math, Course 1, in the ratios and proportional reasoning unit.
Which textbook covers types of ratios?
Reveal Math, Course 1, used in Grade 6, covers part-to-part and part-to-whole ratios in the introduction to ratios chapter.