What is a Fraction?

What is a fraction? Most people have a pretty good idea what numbers are and what they are good for. Sometimes we use them to measure things. Sometimes we use them to label things. Or we use them to put things in order. Or we use them to count things like apples. Here's one apple. Here are a few more. Numbers are great for counting. Now we have, two, three, four, five, six apples. One, two, three, four butterflies. One, two, three, four, five, six, seven, a lot of ping pong balls. Very useful things numbers. Great for counting things. One anvil. Oh, well, now it's all apple sauce. I guess we use what's left of the apples to make a pie. One apple pie. But I can't eat a whole apple pie by myself. Well, I can, but I probably shouldn't. But I can share it with friends. I can cut it in half and give half to my friend. I can eat the other half. So far, no problem. Our normal language has ways of talking about things like halves. We can talk about thirds, quarters, and so on. But I might have more friends, and some of them might be hungrier than others, and I really shouldn't eat half a pie, either. I want to share some of the pie with my friends. Is there a good way to think of these kinds of problems? Is there a kind of number that we can use to count parts and amounts that aren't just whole things? Let's try cutting a pie in a different way. One common math tool we use to talk about these kinds of situations is to use what we call fractions. A fraction is a kind of number that tells how many equal sized pieces of something we have and how many of those pieces it takes to make a whole or complete thing. Let's cut this pie into seven equal sized pieces. I'll have a piece. Thank you very much. And another one of my friends will have two pieces. She didn't have lunch today. To represent this, to write it out, we can use a fraction bar and a couple of numbers. The top number is the number of pieces we have. The bottom number is the number of pieces it takes to make a whole. I am eating one seventh of the pie. My friend is having two sevenths of the pie, and there are four sevenths of the pie left. Enough for at least a couple more friends. Remember, the number on top is the number of pieces someone has. These are called the numerators. The number on the bottom is the number of pieces it takes to make a whole pie. These are called the denominators. If we take all these and add them together, we get seven sevenths or one pie. We can use this system to talk about all kinds of things, not just pies. For example, here's a sack of flour. We can use two and a quarter cups of flour to make some pies. We can have three eighths of a tank of gas left, a board that is two thirds of a meter long, or a piece of tape that can wrap around a box four and three eighths times. And, yes, we can have fractions that are fractions of fractions. It can be fractions all the way down. Using fractions, we can deal with all kinds of situations where we have to divide things up. How might you use fractions in your life?