In this lesson we're going to learn what equivalent fractions are and how to tell if two fractions are equivalent to each other. So what are equivalent fractions? They're fractions that have different numbers but still represent the same value or the same amount. So if we look at these rectangles here, we can see that two out of the three rectangles are shaded in. So we can write this fraction as two thirds. Now let's see what happens if we draw a line down the middle. Now we have six boxes and four out of the six are shaded in. But notice that it still represents the same amount. We haven't increased or decreased the size of the shaded part. So we could say that the two thirds is still equal or equivalent to four six. So how do we know if the fractions are equivalent? One way is that if we multiply or divide the numerator and denominator of one fraction by the same number and it's equal to the other fraction, then those fractions are equivalent. So let's see what that means. These are the same fractions that we had in our first example. So we now already know that they are equivalent. If we multiply the two in the numerator, the first fraction by two, it will give us four in the numerator of the other fraction and the same in the denominator. If we multiply that three times two, we get six. So notice if we multiply the numerator and denominator of that first fraction by two, that's very important. We have to multiply by the same number. It gives us the four over six that we see in the other fraction, so they are equivalent. Let's look at another example. Here we have nine swifts and three four. And the goal here is to try to see if there's a number that we can multiply or divide the first fraction by that will give us the second fraction. So let's see, we have a nine in the numerator of the first fraction and a three in the second fraction. Well, if we divide by three, nine divided by three will give us the three in the other fraction. And if we divide the denominator by 3, 12 divided by three gives us four as well. So if we divide both parts, the numerator and denominator of the first fraction by three, it does give us the second fraction. So that's how we know they are equivalent. Here's a different way for us to tell if the fractions are equivalent. It involves using what we call cross products. If the cross products are equal, then the fractions equivalent. So what's a cross product? We get a cross product when we multiply the two numbers that are on a diagonal from each other. For example, the three and the four here are on a diagonal on a slant from each other. If we multiply the three times four, we get twelve. So that's the cross product of that part of the fractions. Then we do the same thing going the other way. We multiply the two and six that are on a diagonal from each other. That's the other cross product. So two times six also gives us twelve. So both of the cross products are equal to twelve. That tells us that the fractions are equivalent. Let's try it with this one. First, we multiply the twelve times three. That gives us 36 for that cross product. If we go in the other direction, eight times four gives us 32. 32 and 36 are not equal to each other. We got two different numbers. So that means that these fractions are not equivalent. So just to review equivalent fractions or fractions that have different numbers but represent the same value, multiplying or dividing the numerator and denominator both parts of one fraction by the same number equals the other fraction and the cross products of equivalent fractions are equal. So we have those two different ways of testing the fee if the fractions are equivalent.