Ratio of 40 cm to 2 m Step by Step

Step by step

The question

Question: write the ratio of 40 centimeters to 2 meters in its simplest form.

40 cm : 2 m

Careful!

The units are not the same: centimeters and meters.

40 to 2 would compare different things.

Careful: not 40 : 2 ✗

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.

1 m = 100 cm

So 2 meters is 2 times 100: 200 centimeters.

= 2 m = 2 × 100 cm = 200 cm

2 Drop the units

Now the ratio is 40 centimeters to 200 centimeters.

= 40 cm : 200 cm

Both are in centimeters.

The same units cancel, so we cross them out.

That leaves 40 to 200.

= 40 : 200

3 Simplify

40 and 200 can both be divided by 40.

We divide both parts by 40.

The ratio stays the same.

= 40 ÷ 40 : 200 ÷ 40

40 divided by 40 is 1.

200 divided by 40 is 5.

So the ratio is 1 to 5.

= 1 : 5

4 Check

Let's check: times each part by 40.

We get 40 centimeters and 200 centimeters again.

1 × 40 = 40 cm, 5 × 40 = 200 cm

And 200 centimeters divided by 100 is 2 meters, as in the question.

So the answer is right!

200 cm = 200 ÷ 100 = 2 m

Let's look back.

First: same units.

Then: drop the units.

Then: simplify.

Last: check.

Answer