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Dividing Fractions - Don't change that value!

Here's an example: 3/5 divided by 7/8.

    3/5
   _____

    7/8

Let's do it WRONG, to see why that's bad. Here's our example, multiplied by something that ISN'T equal to one:

    3/5      1       3/5      3/5
   _____ * _____ = _______ = ______ = 3/5

    7/8     8/7     56/56      1

Multiplying 7/8 by 8/7 turns our denominator into 1, which seems helpful. But it leaves us with the same numerator we started with. Can this be right? Is 3/5 divided by 7/8 equal to 3/5 divided by one, so that 7/8 = 1? Oops, that has to be wrong.


For comparison, here's the RIGHT way:

    3/5     8/7     24/35     24/35
   _____ * _____ = _______ = _______ = 24/35

    7/8     8/7     56/56       1
 

In this case, what we multiplied by, 8/7 divided by 8/7, is equal to one, because anything divided by itself is equal to one. But 1 over 8/7, which we used up above in the first example, is NOT equal to one, which means that if we use 1 over 8/7, we change our question. We may get an answer, but it won't be the right one.

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