Simplify 45 minutes : 2 hours Step by Step

Step by step

The question

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

45 minutes : 2 hours

Careful!

The units are not the same: minutes and hours.

45 to 2 would compare different things.

Careful: not 45 : 2 ✗

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.

1 hour = 60 minutes

So 2 hours is 2 times 60: 120 minutes.

= 2 hours = 2 × 60 minutes = 120 minutes

2 Drop the units

Now the ratio is 45 minutes to 120 minutes.

= 45 ~~minutes~~ : 120 ~~minutes~~

Both are in minutes.

The same units cancel, so we cross them out.

That leaves 45 to 120.

= 45 : 120

3 Simplify

45 and 120 can both be divided by 15.

We divide both parts by 15.

The ratio stays the same.

= 45 ÷ 15 : 120 ÷ 15

45 divided by 15 is 3.

120 divided by 15 is 8.

So the ratio is 3 to 8.

= 3 : 8

4 Check

Let's check: times each part by 15.

We get 45 minutes and 120 minutes again.

3 × 15 = 45 minutes, 8 × 15 = 120 minutes

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

So the answer is right!

120 minutes = 120 ÷ 60 = 2 hours

Let's look back.

First: same units.

Then: drop the units.

Then: simplify.

Last: check.

Answer