Introduction: Part-to-Part and Part-to-Whole Ratios
This Grade 6 math skill from Pengi Math (Grade 6) introduces part-to-part and part-to-whole ratios. Students learn the difference between comparing one part to another part of a group (part-to-part) versus comparing one part to the total (part-to-whole), and how to write each type of ratio.
Key Concepts
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 $12:15$. The part to whole ratio of boys to students is $15:27$. 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.
Common Questions
What is a part-to-part ratio?
A part-to-part ratio compares one subset of a group to another subset. For example, if there are 3 red balls and 5 blue balls, the part-to-part ratio of red to blue is 3:5.
What is a part-to-whole ratio?
A part-to-whole ratio compares one part of a group to the total. For example, 3 red balls out of 8 total gives a part-to-whole ratio of 3:8.
How are part-to-part and part-to-whole ratios different?
Part-to-part ratios compare two subgroups, while part-to-whole ratios compare one subgroup to the entire group. Both use the same colon or fraction notation.
Can a part-to-whole ratio be converted to a percent?
Yes. Divide the part by the whole and multiply by 100. A ratio of 3:8 means 3/8 = 37.5%.
Where are part-to-part and part-to-whole ratios introduced?
These concepts are introduced in the Grade 6 Pengi Math textbook as a foundation for understanding ratios and proportions.