Why do you have to do those little fractions/ calculations first?

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[Originally posted in Discussions]
Module 1 Week 1 Day 2 Challenge Explanation Part 1
So I ask a lot of questions. But anyways why do you have to do those little fractions/ calculations first? Why not, say, do something else?

That's a good question. You do need to do the little fraction inside the big fraction first. This gets into the meaning of what a fraction or a divide is (and it answers your other question, posted under "Also.").
One way to think of fractions (or divides) is as switchedaround multiplication problems. So in \(\frac{2}{3},\) the "2" means something altogether that you are sharing, and "3" means the number of groups you are sharing them into. For example,
$$\frac{2 \text{ cookies}}{3 \text{ people}} $$.
The answer to this fraction means how much cookie each person gets. As a multiplication problem, this would be:
And you could represent it as a picture of groups, like this:
What if you divide by a fraction, like
Compare this with
There are half as many people, so each person should get more. How much more? They should get twice as much. This is why
This works no matter if the numerator (top number) of the fraction is 1 or any other number.
This also explains why we have to do the little fraction first; we have to know how many people we are sharing the cookies with before we can begin to figure out how many cookies each person gets.
I hope this helps! Let me know if you have any more questions.
Happy Learning!
The Daily Challenge Team