Step by step
The question
Question: write the ratio of 18 inches to 2 yards in its simplest form.
Careful!
The units are not the same: inches and yards.
18 to 2 would compare different things.
1 Same units
A ratio only compares amounts in the same unit.
We change to the smaller unit, inches, so there are no fractions.
1 yard is 36 inches.
So 2 yards is 2 times 36: 72 inches.
2 Drop the units
Now the ratio is 18 inches to 72 inches.
Both are in inches.
The same units cancel, so we cross them out.
That leaves 18 to 72.
3 Simplify
18 and 72 can both be divided by 18.
We divide both parts by 18.
The ratio stays the same.
18 divided by 18 is 1.
72 divided by 18 is 4.
So the ratio is 1 to 4.
4 Check
Let's check: times each part by 18.
We get 18 inches and 72 inches again.
And 72 inches divided by 36 is 2 yards, as in the question.
So the answer is right!
Let's look back.
First: same units.
Then: drop the units.
Then: simplify.
Last: check.