Grade 7 · Unit 1 · Lesson 2 · part 2 of 6
Portion, share, proportional
The word proportional comes from portion , a share.
Portion, share, proportional
The word proportional comes from portion, a share. Think of a pizza cut into equal slices: every slice is the same share of the pizza. In a proportional relationship, every part keeps the same share, which means the same thing as this:
A proportional relationship always multiplies by the same number, the unit rate.
In Lesson 1 you found that number, the unit rate, how much for one. This lesson asks a yes-or-no question about a table: does it always multiply by the same number, or not?
Here are two tables. Lemonade is $0.75 a cup. Bowling is $8 for one game, and you also pay $3 to rent shoes, no matter how many games you play.
| Cups (input) | Cost (output) | Output ÷ input |
|---|---|---|
| 1 | $0.75 | 0.75 ÷ 1 = 0.75 |
| 2 | $1.50 | 1.50 ÷ 2 = 0.75 |
| 3 | $2.25 | 2.25 ÷ 3 = 0.75 |
| 4 | $3.00 | 3.00 ÷ 4 = 0.75 |
| Games (input) | Cost (output) | Output ÷ input |
|---|---|---|
| 1 | $8 | 8 ÷ 1 = 8 |
| 2 | $13 | 13 ÷ 2 = 6.5 |
| 3 | $18 | 18 ÷ 3 = 6 |
Lemonade: every row divides to 0.75. The same number, every time. Proportional. The relationship always multiplies by 0.75: cups times 0.75 gives the cost.
Bowling: the rows divide to 8, then 6.5, then 6. Different numbers. Not proportional. Why? That $3 shoe fee. It is there even if you play zero games, so zero games does not cost zero dollars. A proportional relationship always starts at nothing for nothing: 0 cups of lemonade cost $0.