Ratio of 3 m to 50 cm

Step by step

The question

Question: write the ratio of 3 meters to 50 centimeters in its simplest form.

Careful!

The units are not the same: meters and centimeters.

3 to 50 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 300 centimeters to 50 centimeters.

Both are in centimeters.

The same units cancel, so we cross them out.

That leaves 300 to 50.

3 Simplify

300 and 50 can both be divided by 50.

We divide both parts by 50.

The ratio stays the same.

300 divided by 50 is 6.

50 divided by 50 is 1.

So the ratio is 6 to 1.

4 Check

Let's check: times each part by 50.

We get 300 centimeters and 50 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.