Ratio of 500 g to 2 kg Step by Step

Step by step

The question

Question: write the ratio of 500 grams to 2 kilograms in its simplest form.

500 g : 2 kg

Careful!

The units are not the same: grams and kilograms.

500 to 2 would compare different things.

Careful: not 500 : 2 ✗

1 Same units

A ratio only compares amounts in the same unit.

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

1 kilogram is 1000 grams.

1 kg = 1000 g

So 2 kilograms is 2 times 1000: 2000 grams.

= 2 kg = 2 × 1000 g = 2000 g

2 Drop the units

Now the ratio is 500 grams to 2000 grams.

= 500 g : 2000 g

Both are in grams.

The same units cancel, so we cross them out.

That leaves 500 to 2000.

= 500 : 2000

3 Simplify

500 and 2000 can both be divided by 500.

We divide both parts by 500.

The ratio stays the same.

= 500 ÷ 500 : 2000 ÷ 500

500 divided by 500 is 1.

2000 divided by 500 is 4.

So the ratio is 1 to 4.

= 1 : 4

4 Check

Let's check: times each part by 500.

We get 500 grams and 2000 grams again.

1 × 500 = 500 g, 4 × 500 = 2000 g

And 2000 grams divided by 1000 is 2 kilograms, as in the question.

So the answer is right!

2000 g = 2000 ÷ 1000 = 2 kg

Let's look back.

First: same units.

Then: drop the units.

Then: simplify.

Last: check.

Answer