Let’s compare fractions with different numerators and denominators. But first, I need to tell you a story. This is Mr Smith’s class and this is Mrs Jones’s class. But we’re gonna call them the blue team and the red team. We wanna find out if
Mr [Mrs] Jones’s or Miss [Mr] Smith’s class is stronger. So we’re gonna choose one-fourth of the blue team and one-fourth of the red team. And we’re gonna find out which class is stronger.
The two teams lined up to play their game and the blue team seemed very happy, but the red team was a little bit upset. Even though they both had one-fourth of their players on the field, the red team only had four players on the field and the blue team had five. You see the blue team had twenty people to start with. And the red team only had sixteen people to start with. One-fourth of twenty people is five, but one-fourth of sixteen people is only four.
This story shows us that we can only compare fractions when the wholes are the same. In this case, the whole blue team had twenty people and the whole red team had sixteen. So, our comparison didn’t work.
Here’s another example of that. Cody ate a whole pizza for lunch. Kathryn ate a whole pizza for lunch. Compare the amount that they ate. So you think one whole pizza equals one whole pizza. But then you remember red team versus blue team. And so you say, wait a minute! What were the sizes of the pizzas? Here are their pizzas. Cody ate eight out of eight slices and so did Kathryn; they both ate one whole pizza.
But using fractions doesn’t work to compare these. So we remembered that comparing fractions work when the two fractions refer to the same whole amount So now we wanna compare one-fourth and three-fourths of two equally sized objects. Remember that when we’re comparing, we’re gonna use greater than, less than, or equal to.
Let’s look at the two pictures below to solve the problem. By looking at the picture, we can tell that one-fourth is less than three-fourths. When each of our fractions are out of the same amount of parts, here each rectangle is cut into four parts, it’s very easy to see which one is more and which one is less.
Let’s try a problem, where are blocks are the same size, but they’re cut into different amount of pieces. So, we drew a picture of block A and block B. And then we’re gonna shade in the fraction that it represents. When we compare the shading, four-eighths of block A and one-half of block B, we can see that they are equal amounts. Four-eighths equals one-half.
Let’s try another one. Let’s compare three-sixths to five-eighths. The first step is to shade each rectangle. Then, you can see which fraction is bigger. We have three-sixths is less than five-eighths.
Okay, I want you to try this one. Compare two-thirds and three-eighths. If you aren’t sure where to start, start by drawing two equally sized rectangles. Divide the first one in three parts and the second one into eight parts. Two-thirds is greater than three-eighths; let’s see why. When we drew our picture and shaded in each fraction, it was very clear to us that two-thirds was much more than three-eighths.
So, what should you remember? You should remember that comparing fractions work when the two fractions refer to the same whole amount. So, we always need to check and see the size of the two objects we’re working with. Well, also remember that we can use models when we’re comparing. And finally, when we compare fractions, the outcomes can be greater than, less than, or equal to.