Ratio of 1 km to 400 m Step by Step

Step by step

The question

Question: write the ratio of 1 kilometer to 400 meters in its simplest form.

1 km : 400 m

Careful!

The units are not the same: kilometers and meters.

1 to 400 would compare different things.

Careful: not 1 : 400 ✗

1 Same units

A ratio only compares amounts in the same unit.

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

1 kilometer is 1000 meters.

1 km = 1000 m

So 1 kilometer is 1 times 1000: 1000 meters.

= 1 km = 1 × 1000 m = 1000 m

2 Drop the units

Now the ratio is 1000 meters to 400 meters.

= 1000 m : 400 m

Both are in meters.

The same units cancel, so we cross them out.

That leaves 1000 to 400.

= 1000 : 400

3 Simplify

1000 and 400 can both be divided by 200.

We divide both parts by 200.

The ratio stays the same.

= 1000 ÷ 200 : 400 ÷ 200

1000 divided by 200 is 5.

400 divided by 200 is 2.

So the ratio is 5 to 2.

= 5 : 2

4 Check

Let's check: times each part by 200.

We get 1000 meters and 400 meters again.

5 × 200 = 1000 m, 2 × 200 = 400 m

And 1000 meters divided by 1000 is 1 kilometer, as in the question.

So the answer is right!

1000 m = 1000 ÷ 1000 = 1 km

Let's look back.

First: same units.

Then: drop the units.

Then: simplify.

Last: check.

Answer