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.
