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Dear Math:

Can you help me learn how to multiply fractions? I know that when you multiply two numbers, you always end up with a bigger number. So I know I'm getting the wrong answer when I get a smaller result than either of the numbers I started with. Thinking about this makes me positively dizzy.

Sincerely, 

Lucille Austero

Ms. Austero, I have some good news. You should get a smaller number when you multiply two fractions.

Let's start off with this problem:

When you multiply 1/2 by 1, you know you are going to get 1/2, right? After all, anything times 1 equals itself.

But let's say you multiplied 1/2 times less than 1. Doesn't it make sense that your answer is going to end up being less than 1/2?

So let's apply our technique here for multiplying fractions. Just multiply across the top, then multiply across the bottom:

Then simplify (you don't want overly-noisy fractions, after all):

And your result comes out nice, simplified, and less than your original fraction.

It's the way it should be! We will practice this a few times this week, so you can get a feel for it. But just know, you haven't done anything wrong if you end up with something smaller than you had at the beginning.