Math 7 · Unit 3, Lesson 7: Rational Number Problems · Tile 3 of 4
Sharing the Prize
A fair share is a proportion
Fair is not always equal
Sometimes fair doesn't mean equal. If one group did more of the work, it should get more of the prize. Find each group's fraction of the total work, then give it that same fraction of the prize. That's a proportional relationship, the same idea from Unit 1.
To share a quantity proportionally, multiply it by each part's fraction of the whole.
Each group's share of the prize matches its share of the work. Same fraction, both times.
A proportional relationship always multiplies by the same number, the unit rate.
Here the unit rate is the prize money per box top.
Watch it work
Sharing prize money. Three 7th grade classes won a $600 prize for collecting box tops. Mr. Aceves' class collected 3,760, Mrs. Baca's class 2,301, and Mr. Canyon's class 1,855. How should they split the money so each class gets the same fraction of the prize as its fraction of the box tops?
A calculator is fine on this tile.
Round each share to the cent, and round at the last step.
The same problem with the unit rate
600 ÷ 7,916 is about $0.0758 per box top. Then multiply each class's box tops by that rate.
Both ways give the same answer.
NC standard: NC.7.NS.3.