Step by step
The question
Question: write the ratio of 6 days to 2 weeks in its simplest form.
Careful!
The units are not the same: days and weeks.
6 to 2 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 2 weeks is 2 times 7: 14 days.
2 Drop the units
Now the ratio is 6 days to 14 days.
Both are in days.
The same units cancel, so we cross them out.
That leaves 6 to 14.
3 Simplify
6 and 14 can both be divided by 2.
We divide both parts by 2.
The ratio stays the same.
6 divided by 2 is 3.
14 divided by 2 is 7.
So the ratio is 3 to 7.
4 Check
Let's check: times each part by 2.
We get 6 days and 14 days again.
And 14 days divided by 7 is 2 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.