Step by step
The question
Question: write the ratio of 3 weeks to 6 days in its simplest form.
Careful!
The units are not the same: weeks and days.
3 to 6 would compare different things.
1 Same units
A ratio only compares amounts in the same unit.
We change to the smaller unit, days, so there are no fractions.
1 week is 7 days.
So 3 weeks is 3 times 7: 21 days.
2 Drop the units
Now the ratio is 21 days to 6 days.
Both are in days.
The same units cancel, so we cross them out.
That leaves 21 to 6.
3 Simplify
21 and 6 can both be divided by 3.
We divide both parts by 3.
The ratio stays the same.
21 divided by 3 is 7.
6 divided by 3 is 2.
So the ratio is 7 to 2.
4 Check
Let's check: times each part by 3.
We get 21 days and 6 days again.
And 21 days divided by 7 is 3 weeks, as in the question.
So the answer is right!
Let's look back.
First: same units.
Then: drop the units.
Then: simplify.
Last: check.