Worked examples
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.
▶ Watch it solved
The question
Question: write the ratio of 45 minutes to 2 hours in its simplest form.
45 minutes : 2 hours
Careful!
The units are not the same: minutes and hours.
45 to 2 would compare different things.
Careful: not 45 : 2 ✗
1 Same units
A ratio only compares amounts in the same unit.
We change to the smaller unit, minutes, so there are no fractions.
1 hour is 60 minutes.
1 hour = 60 minutes
So 2 hours is 2 times 60: 120 minutes.
= 2 hours = 2 × 60 minutes = 120 minutes
2 Drop the units
Now the ratio is 45 minutes to 120 minutes.
= 45 minutes : 120 minutes
Both are in minutes.
The same units cancel, so we cross them out.
That leaves 45 to 120.
= 45 : 120
3 Simplify
45 and 120 can both be divided by 15.
We divide both parts by 15.
The ratio stays the same.
= 45 ÷ 15 : 120 ÷ 15
45 divided by 15 is 3.
120 divided by 15 is 8.
So the ratio is 3 to 8.
= 3 : 8
4 Check
Let's check: times each part by 15.
We get 45 minutes and 120 minutes again.
3 × 15 = 45 minutes, 8 × 15 = 120 minutes
And 120 minutes divided by 60 is 2 hours, as in the question.
So the answer is right!
120 minutes = 120 ÷ 60 = 2 hours
Let's look back.
First: same units.
Then: drop the units.
Then: simplify.
Last: check.
▶ Watch it solved
The question
Question: write the ratio of 1.5 kilograms to 600 grams in its simplest form.
1.5 kg : 600 g
Careful!
The units are not the same: kilograms and grams.
1.5 to 600 would compare different things.
Careful: not 1.5 : 600 ✗
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 1.5 kilograms is 1.5 times 1000: 1500 grams.
= 1.5 kg = 1.5 × 1000 g = 1500 g
2 Drop the units
Now the ratio is 1500 grams to 600 grams.
= 1500 g : 600 g
Both are in grams.
The same units cancel, so we cross them out.
That leaves 1500 to 600.
= 1500 : 600
3 Simplify
1500 and 600 can both be divided by 300.
We divide both parts by 300.
The ratio stays the same.
= 1500 ÷ 300 : 600 ÷ 300
1500 divided by 300 is 5.
600 divided by 300 is 2.
So the ratio is 5 to 2.
= 5 : 2
4 Check
Let's check: times each part by 300.
We get 1500 grams and 600 grams again.
5 × 300 = 1500 g, 2 × 300 = 600 g
And 1500 grams divided by 1000 is 1.5 kilograms, as in the question.
So the answer is right!
1500 g = 1500 ÷ 1000 = 1.5 kg
Let's look back.
First: same units.
Then: drop the units.
Then: simplify.
Last: check.
▶ Watch it solved
