Ratio of 80 cm to 3 m

Step by step

The question

Question: write the ratio of 80 centimeters to 3 meters in its simplest form.

Careful!

The units are not the same: centimeters and meters.

80 to 3 would compare different things.

1 Same units

A ratio only compares amounts in the same unit.

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

1 meter is 100 centimeters.

So 3 meters is 3 times 100: 300 centimeters.

2 Drop the units

Now the ratio is 80 centimeters to 300 centimeters.

Both are in centimeters.

The same units cancel, so we cross them out.

That leaves 80 to 300.

3 Simplify

80 and 300 can both be divided by 20.

We divide both parts by 20.

The ratio stays the same.

80 divided by 20 is 4.

300 divided by 20 is 15.

So the ratio is 4 to 15.

4 Check

Let's check: times each part by 20.

We get 80 centimeters and 300 centimeters again.

And 300 centimeters divided by 100 is 3 meters, as in the question.

So the answer is right!

Let's look back.

First: same units.

Then: drop the units.

Then: simplify.

Last: check.