Types of Fractions

Types of fractions. What are the different types of fractions? To answer that, we'll start with a pie. Now, we'll cut it into three pieces. We'll take away a piece, and what's left is two thirds of a pie. We can write this into 2/3. When we write a fraction this way, we have two numbers, one above the other. And between them, we have a bar, the top number, which we call the numerator, and the bottom number, which we call the denominator. The numerator tells us the number of equal sized pieces that we have in the whole Pi. In this case, the pi was sliced into three pieces, but we only have two of them here now. The denominator tells us how many of those equal sized pieces it takes to make up a whole. Of the three pieces we have left, we now have only two or two thirds. In this case, the amount of pie we have left is less than a whole pie. So the numerator is smaller than the denominator. When this is true, we call this type of fraction a proper fraction. There's a bakery stall at the local market that specializes in pies. When a fresh pie comes out of the oven, it gets sliced into eight pieces. Some of the pies are sold as whole pies. Once they are sliced, all eight pieces go into a pie box. Other pies are separated, and each slice is put into its own individual box. You can buy a whole pie or you can buy a pie by the slice. It's cheaper per slice to buy the whole pie, and there's less packaging. Good for the planet, right? But if you only need a slice or two, then you can buy them individually. No need to keep eating pie till you're sick of it. Here's Joe. He's having a party and has several friends coming over. He needs something for dessert. The baker asks, how many friends are coming? Joe says he has ten friends coming to the party plus himself. So he'll buy 11 slices. Okay, here comes the fraction. Since each slice is one eighth of a pie, Joe's wanting to buy 11 eighths of a pie. Oh, oh, look at that fraction. The numerator is bigger than the denominator. When that happens, we call that an improper fraction. And it means that we have more than one whole pie. Hey, wait a minute. Oh, no. What a disaster. It'll be cheaper to buy a whole pie and three slices. We're not made of money. And what about all that extra packaging? Oh, my goodness. What a waste. Joe's going to buy a whole pie and three single slices. We can write that as one and three eighths. This is called a mixed number. It's a whole number and a fraction together. The one is the whole part. In this case, a whole pie. And the three eighths is the fractional part of the mixed number. One and three eighths is the same as 11 eighths. In this case, it's 11 slices either way. But sometimes it's easier or better to think of an improper fraction as a mixed number. In this case, it saved Joe some money and kept some extra packaging out of the landfill. A mixed number is the same as taking the whole number part and adding the fraction to it. And that anytime a fraction has the same number for the numerator and the denominator, it's equal to one. 8/8 is just another way of saying one. So the numbers still add up to 11 eighths. To summarize, when the numerator is smaller than the denominator, this is called a proper fraction. When the numerator is bigger than the denominator, this is called an improper fraction. And when we have a whole number and a fraction together, this is called a mixed number.