Ratio of 90 seconds to 2 minutes Step by Step

Step by step

The question

Question: write the ratio of 90 seconds to 2 minutes in its simplest form.

90 seconds : 2 minutes

Careful!

The units are not the same: seconds and minutes.

90 to 2 would compare different things.

Careful: not 90 : 2 ✗

1 Same units

A ratio only compares amounts in the same unit.

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

1 minute is 60 seconds.

1 minute = 60 seconds

So 2 minutes is 2 times 60: 120 seconds.

= 2 minutes = 2 × 60 seconds = 120 seconds

2 Drop the units

Now the ratio is 90 seconds to 120 seconds.

= 90 ~~seconds~~ : 120 ~~seconds~~

Both are in seconds.

The same units cancel, so we cross them out.

That leaves 90 to 120.

= 90 : 120

3 Simplify

90 and 120 can both be divided by 30.

We divide both parts by 30.

The ratio stays the same.

= 90 ÷ 30 : 120 ÷ 30

90 divided by 30 is 3.

120 divided by 30 is 4.

So the ratio is 3 to 4.

= 3 : 4

4 Check

Let's check: times each part by 30.

We get 90 seconds and 120 seconds again.

3 × 30 = 90 seconds, 4 × 30 = 120 seconds

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

So the answer is right!

120 seconds = 120 ÷ 60 = 2 minutes

Let's look back.

First: same units.

Then: drop the units.

Then: simplify.

Last: check.

Answer