Now that we know how to use fractions to represent parts of a whole, there’s a few different things we can do with them. First of all, we can compare fractions. Comparing fractions means checking to see if one fraction is greater than, less than, or equal to another fraction. That’s pretty easy if we think of fractions as parts of objects, and draw pictures to help us see what we have. Here’s an example… Which of these fractions is greater: three-eights or five-eights ? To answer that question, let’s start by drawing two rectangles and divide them into eight equal parts. Since the rectangles are divided into eight parts, each of those parts are called an eighth. Now, let’s shade three parts of the first rectangle… or three-eighths, and five parts of the second rectangle… or five-eighths. Our picture makes comparing these fractions easy. You can see that five-eighths is greater than three-eights, because more of that rectangle is shaded. Okay, now let’s try one that’s a little harder. Which of these fractions is greater: three-fourths or four-fifths ? Well, let’s start again with two rectangles, but this time, we need to divide them up differently because the fractions we are comparing have different bottom numbers. The first rectangle will be divided into four equal parts, and we’ll shade three of them to show three-fourths. The second rectangle will be divided into five equal parts, and we’ll shade four of them to represent four-fifths. Now to compare, all we have to do is see which rectangle is shaded in the most, and that tells us that four-fifths is greater than three-fourths. There… that wasn’t so hard after all. Alright, let’s try one more example. Let’s compare the fractions one-half and two-fourths. Again, we start by drawing rectangle and dividing them up into parts: two on this one, and four on this one. Next, we shade the parts of the rectangle according to our top numbers: one on this one, and two on this one. Now, all we have to do is compare. Well, what do ya know? The same amount of each rectangle is shaded. That means these two fractions are equal! It might seem strange that two fractions can have totally different numbers and still represent the same amount, but they can! Fractions like that are called ‘Equivalent Fractions’. Equivalent fractions have different top and bottom numbers, but are equal in value. We’ll learn more about equivalent fractions later in this video, but for now, let’s find out what else we can do with fractions. Another thing we can do with fractions is add them together. Any two fractions can be added, but for now, we’re only going to add fractions if they have the same bottom numbers, because those fractions are much easier to add. …like these two fractions: one-fourth and two-fourths. Let’s add them together. Again, we can use drawings to help us solve this problem. Looking at the rectangles for these two fractions, we can add them visually just by rearranging the parts. Because all of the parts are ‘fourths’, our answer will also be ‘fourths’. We can just take this one-fourth from over here, and combine it with these two-fourths, and ta-da… three-fourths! So, one-fourth plus two-fourths equals three-fourths. Let’s try another one. Let’s add three-eights to five-eights. We can use any shape we want, so I’m gonna use a circle this time. So we have three out of eight here, and five out of eight here. Just like our last problem, we can add these by combining the parts. So let’s put these three over here with these five. Well what do ya know?… That fills up all eight sections. So three-eights plus five-eights equals eight-eights (or one whole circle). In those examples, you might have noticed a pattern. The bottom number of our answer was always the same as the bottom numbers of the fractions we were adding. And the top number of our answer was just the sum of the top numbers of those fractions. Well, that’s how it works. That’s the procedure (or set of steps) for adding fractions that have the same bottom numbers. That’s important, because if you can remember that procedure, then you won’t need to use drawings to help you add fractions. And that’s a really good thing, because what if you had to add these two fractions together: fifteen-hundredths and ten hundredths. It would be WAY too much work to draw rectangles and divide them up into 100 parts! Fortunately, since we know the procedure for adding fractions, we can do it without the drawings. First, let’s write out the problem. Now… because we’re adding fractions, we know the answer will also be a fraction. The bottom number of our answer will be the same as the bottom number of the fractions we’re adding: 100. And the top number of our answer will just be the sum of our top numbers: 15 plus 10, which equals 25. So as you can see, adding fractions with the same bottom numbers is easy when you know the procedure. All of this brings up a really important point. When you’re first learning about fractions, drawing pictures and imagining that fractions represent parts of cookies and candy bars can be really useful. (And it can taste good too!) Thinking of them that way can help you understand how simple fractions work, and it can even help you solve some basic math problems. But soon, you’ll have to do harder math problems! And to solve those, you’ll need to stop thinking about fractions as just parts of things, and start thinking about them in a different way. And that’s what we are going to be talking about in the next section. Before we move on, let’s review what we’ve covered so far. We can draw pictures to show how fractions represent parts of a whole. Using drawings, we can compare fractions to see which one represents the greatest amount. If we compare two different fractions and find that they represent the same amount, then we call them equivalent fractions. We can also use drawings to help us do simple addition by combining the parts. By doing this, we learned that the procedure for adding fractions that have the same bottom number, is to just add the top numbers and keep the same bottom number in our answer. Now to make sure you understand how to compare and add fractions visually, be sure to do the exercises for this section. learn more at www.mathantics.com

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