Divide and Conquer

Mr. C:

You always say that "every fraction is a division problem." What do you mean by this? I always thought that every fraction was a fraction. I'm so baffled. 

Your biggest fan,

Cash Flagg

Cash:

Yes, one thing that I have always tried to drive home is the fact that every fraction is a division problem. What I mean by this is that it is true! 

Let's take a look at 13/4. First off, he's walking along, walking along, and uh-oh! He fell over! Now you have your division problem all set up.

 

Now, you just take 4 into 13. You get a remainder of 1, but don't treat it like a "leftover" remainder, turn it into a fraction...just a smaller one. put the 1 over the divisor, and now you have 1/4.

 

Let's take a look at one that isn't top-heavy this time. In fact, let's take that 1/4, and just turn that into a division problem. 

Just like the first fraction, this one is walking along and falls over...and it becomes an interesting-looking division problem. But you know what? It's still every bit as much a division problem. 

1 can't go into 4.

Or can it?

This is when we have to call in our friends, the Phantom Zeroes. Phantom Zeroes are always there, but you can't always see them. The only time they show up is when we need them.

This time, we're going to just show two of them, but the best thing is that you can always add more and more if you need to.

Don't forget to put the decimal there right after the 1. Make sure it rises straight up above the division line. 

You can see, when you work the problem out, you get .25, as in 25 cents! In other words, 1/4 of a dollar! You see? It's a quarter. 

Finally, let's look at this one. This is a very top-heavy fraction. But it's going to tip over just like any other fraction.

And it's going to work out just like any other division problem. 

I promise I did not mean for this one to come out evenly when I made it. It was a happy accident.

Any time you need to simplify a fraction, figure out what the mixed number version is, or figure out what the decimal form is, don't forget, every fraction is a division problem.

Always.