Okay, so far we’ve learned how fractions represent parts of things,
and we’ve learned how to do some simple math with those parts.
But if we want to really understand how fractions work, we need to start thinking about them in a new way.
We need to learn what a fractions really are.
A fraction is just a number that’s written like a division problem.
You remember division right? …where you take one number and divide it up by another number.
And you might also remember that there’s different ways to write a division problem.
When you first learn about division, you usually see division problems written like this…
Now that symbol in the middle just means divide this number by that number.
Then you learn it’s useful to write a division problem a different way…like this.
Now that’s still the same division problem. It just uses a different symbol to tell us to divide.
So that’s two different ways to write the same division problem. But wait…there’s more!
Now some of you who use computers a lot might have seen division written like this…
Now that ‘slash’ is just another way to write the division symbol.
Now this one’s interesting…
Watch what happens when we rearrange it a little bit… Look familiar?
Yep, it’s a division problem that looks like a fraction.
And that’s just because, a fraction really is a division problem, but we treat it like a number.
The line between the top and bottom numbers is just another ay of writing the division symbol!
The top number is the number being divided up, and we call it the ‘numerator’.
The bottom number is the number we’re dividing by, and we call it the ‘denominator’.
Now let’s look at some of the common fractions that you’re already familiar with
and think of them as division problems.
For example, one-half (or one over two) is really just one divided by two.
The fraction two-thirds (or two over three) really means two divided by three.
And the fraction three-fourths (or three over four) really means three divided by four.
Thinking about fractions like little division problems might seem strange to some of you,
especially because these division problems show smaller numbers being divided by larger numbers.
You may not have seen that before. You might not have even thought it was possible.
But you CAN divide a smaller number by a bigger one.
It just means that the answer you get is going to be smaller than one.
If the idea of dividing a smaller number by a bigger one seems confusing to you, don’t worry.
It’s going to make more sense in the next section when we learn about decimal numbers and how they are related to fractions.
Let’s review what we’ve learned so far.
This section was short, but in it, we learned the most important thing there is to know about fractions.
We learned that fractions are numbers that are written like division problems.
The line between the top and bottom numbers is another form of the division symbol.
That tells you to divide the top number by the bottom number.
The top number is called the numerator and the bottom number is called the denominator.
It might be a new idea to you, but you can divide a smaller number by a bigger number.
This was a really important concept we covered, so be sure to do the exercises before you move on.
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