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

  • ADMIN M0★ M1 M5

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  • ADMIN M0★ M1 M5

    [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?

  • ADMIN M0★ M1 M5

    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 switched-around 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:

    56099215-1875-4ab6-baa2-baacf8f2b054-image.png

    And you could represent it as a picture of groups, like this:

    3e261b13-fc3b-4fe0-9b1b-c0171daa04de-image.png

    What if you divide by a fraction, like

    dcd13970-d10e-406f-9690-a99abb4a21e8-image.png

    Compare this with

    b462be17-db96-4474-8d79-c727d658be8e-image.png

    There are half as many people, so each person should get more. How much more? They should get twice as much. This is why

    c793a44c-da5f-4bfb-b6d1-dfe2f6cb9690-image.png

    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