Fractions & Decimals

Depth · one concept from first principles · step 2 of 4

A percent is a rate out of 100

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$78$	$45$	$69$	$108$

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

2STEP 2

Write the part over the base

School B has 45 of those 300 students.

45/300

3STEP 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

Answer

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

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▶ Practice — 12 problems