Lucky

Mr. C,

I'm sitting here thinking about stuff. I'm wondering if there is any way you can make multiplying fractions a little easier. It just takes forever!

Sincerely, 
Brandi Finegirl

Well, Brandi, the bad news is that for many problems involving fractions, there is no really good shortcut. You're going to find that most of them are pretty time-consuming. However, you can use a trick or two to make things a little easier on you.

Before we get to some really time-consuming fraction multiplication, I want to show you one way that can make the process a little bit easier.

At this point in doing math problems, we know that you can simplify a fraction like 3/9 by dividing the numerator and denominator both by 3, giving you 1/3.

Now let's see how this applies to multiplying fractions...

Here we have two fractions, neither of which can be simplified on its own. We have to multiply them. We could do this with no problem as it is. 

However, looking at the numbers, it looks like I could simplify 4 over 10. That could be simplified down to 2 over 5. Because we are multiplying, we can cross-simplify.  This wouldn't work if we were adding or subtracting, by the way.

And then, it looks like you could also cross-simplify 9 over 15. That can simplify down to 3 over 5. 

Now, you just multiply across the top, and multiply across the bottom just the same. 

Now, let's check if it would work the same way even if we didn't cross-simplify. 4*9 is 36. 15*10 is 150. 

Now we just simplify the end product...looks like we can divide the numerator and denominator both by 3, giving us 12/50. Then with that one, we can divide the numerator and denominator both by 2, giving us 6/25, just like the answer we got the first time.

Woohoo! It works!