Step by step
The question
Question: write the ratio of 2.5 meters to 75 centimeters in its simplest form.
Careful!
The units are not the same: meters and centimeters.
2.5 to 75 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 2.5 meters is 2.5 times 100: 250 centimeters.
2 Drop the units
Now the ratio is 250 centimeters to 75 centimeters.
Both are in centimeters.
The same units cancel, so we cross them out.
That leaves 250 to 75.
3 Simplify
250 and 75 can both be divided by 25.
We divide both parts by 25.
The ratio stays the same.
250 divided by 25 is 10.
75 divided by 25 is 3.
So the ratio is 10 to 3.
4 Check
Let's check: times each part by 25.
We get 250 centimeters and 75 centimeters again.
And 250 centimeters divided by 100 is 2.5 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.