# Unit 2 Family Materials

Introducing Proportional Relationships

### Representing Proportional Relationships with Tables

This week your student will learn about proportional relationships. This builds on the work they did with equivalent ratios in grade 6. For example, a recipe says “for every 5 cups of grape juice, mix in 2 cups of peach juice.” We can make different-sized batches of this recipe that will taste the same.

The amounts of grape juice and peach juice in each of these batches form equivalent ratios.

The relationship between the quantities of grape juice and peach juice is a proportional relationship. In a table of a proportional relationship, there is always some number that you can multiply by the number in the first column to get the number in the second column for any row. This number is called the constant of proportionality.

In the fruit juice example, the constant of proportionality is 0.4. There are 0.4 cups of peach juice per cup of grape juice.

Using the recipe “for every 5 cups of grape juice, mix in 2 cups of peach juice”

1. How much peach juice would you mix with 20 cups of grape juice?
2. How much grape juice would you mix with 20 cups of peach juice?

Solution:

1. 8 cups of peach juice. Sample reasoning: We can multiply any amount of grape juice by 0.4 to find the corresponding amount of peach juice, $20 \boldcdot (0.4) = 8$.
2. 50 cups of grape juice. Sample reasoning: We can divide any amount of peach juice by 0.4 to find the corresponding amount of grape juice, $20 \div 0.4 = 50$.