Step by step
The question
Question: write the ratio of 2 hours to 40 minutes in its simplest form.
Careful!
The units are not the same: hours and minutes.
2 to 40 would compare different things.
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.
So 2 hours is 2 times 60: 120 minutes.
2 Drop the units
Now the ratio is 120 minutes to 40 minutes.
Both are in minutes.
The same units cancel, so we cross them out.
That leaves 120 to 40.
3 Simplify
120 and 40 can both be divided by 40.
We divide both parts by 40.
The ratio stays the same.
120 divided by 40 is 3.
40 divided by 40 is 1.
So the ratio is 3 to 1.
4 Check
Let's check: times each part by 40.
We get 120 minutes and 40 minutes again.
And 120 minutes divided by 60 is 2 hours, as in the question.
So the answer is right!
Let's look back.
First: same units.
Then: drop the units.
Then: simplify.
Last: check.