Write 45 minutes : 2 hours as a ratio in its simplest form.

Step by step

The question

Question: write the ratio of 45 minutes to 2 hours in its simplest form.

Careful!

The units are not the same: minutes and hours.

45 to 2 would compare different things.

1 Same units

A ratio only compares amounts in the same unit.

We change to the smaller unit, minutes, so there are no fractions.

1 hour is 60 minutes.

So 2 hours is 2 times 60: 120 minutes.

2 Drop the units

Now the ratio is 45 minutes to 120 minutes.

Both are in minutes.

The same units cancel, so we cross them out.

That leaves 45 to 120.

3 Simplify

We need a number that goes into both parts.

We divide by small numbers that go into both, until none is left.

We used 3 and 5.

Together: 3 times 5 is 15.

We divide both parts by 15.

The ratio stays the same.

45 divided by 15 is 3.

120 divided by 15 is 8.

So the ratio is 3 to 8.

4 Check

Let's check: times each part by 15.

We get 45 minutes and 120 minutes again.

And 120 minutes divided by 60 is 2 hours, as in the question.

So the answer is right!

Let's look back.

First: same units.

Then: drop the units.

Then: simplify.

Last: check.