Problem
A percent is a rate out of 100
A table lists how many students came from each school. We need the percent chance that one student picked at random comes from a particular school.
Ratios
Your answer
How to solve
Strategy Analyze the Units — A percent is a rate whose base is 100, so the work is to decide what the base is and then rewrite the fraction with 100 underneath.
1STEP 1
Find the base
The representative is picked from every student, so the base is the total of all four schools.
78 + 45 + 69 + 108 = 300
There are 300 students in all.
6.RP.A.3Identify SubproblemsThe base is every student at the meet, not one school.
Why?
The representative is picked from all the students together, so the group the chance is measured against is that whole group.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
The four schools have no student in common and leave nobody out, so their counts add to the whole group.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
2STEP 2
Write the part over the base
School B has 45 of those 300 students.
45/300
That fraction is the rate.
6.RP.A.3Analyze The Units3STEP 3
Rewrite it with 100 underneath
A percent is a rate out of 100, so divide the fraction out and multiply by 100.
45 ÷ 300 = 0.15, 0.15 × 100 = 15
It is 15%.
6.RP.A.3Organize Information In More WaysAnswer
15%
Check by scaling: 45/300 is 15/100 once both parts are divided by 3.
Takeaway
A percent is a rate whose base is 100 -- so first decide what the base actually is.
- Find the base
- Write the part over the base
- Rewrite it with 100 underneath