27 of 75 runners finish in under an hour. About how many of 1,500…

Step by step

The question

Question: 27 of 75 runners finish in under an hour.

About how many of 1,500 finish in under an hour?

1 The fraction in the sample

27 out of 75: that is 27/75.

The 75 runners are a sample: a small group that stands for everyone.

27 and 75 can both be divided by 3.

So it is 9/25.

2 Use it for everyone

We expect the same fraction of all 1,500: 9/25 of 1,500.

Of means times.

1,500 divided by 25 is 60.

Then times 9.

That is about 540.

Careful!

A sample only shows about how many.

So the answer is a good guess, not an exact count.

So about 540 runners finish in under an hour.

3 Check

Let's check: 540 out of 1,500.

Divide the top and the bottom by 60: 9/25, the same fraction as the sample.

So the answer is right!

Let's look back.

First: the fraction in the sample.

Then: use it for everyone.

Last: check.