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