Now we're going to learn how to identify whether or not ratios are proportional. So in these problems, we're going to be given two ratios setup as fractions. And our job will be to determine if they are proportional to each other. For our first example, we have to determine whether five over eight is proportional to 15 over 24. And we're going to look at three different methods for determining whether the ratios are proportional. For our first method, we're going to make the fractions have a common denominator. So here's our two fractions and we have a question mark over our equal sign because we're not sure if they are equal to each other or not. And remember that's our goal here. Fractions are proportional if they are equivalent. So let's make these fractions have a common denominator. Well, the least common multiple of eight and 24 is 24. So we can make both of these fractions have 24 as their denominator. And the one on the right already has 24 as its denominator. So for the fraction on the left, we can multiply its denominator by three because three times eight would give us 24. But we also need to multiply the numerator by the same number. We always have to multiply both parts of the fraction by the same number. And if we do that, this fraction becomes 15 over 24. And now let's see if it is equivalent to our other fraction. And it is. These fractions are equivalent, so that means that our ratios are proportional. Here's our second example. Determine whether two over five is proportional to seven over nine. And here we're going to find the cross products to determine whether they're proportional. So if we set up our fractions here, we're going to find what the cross products of them are. And remember, cross products mean that we're taking the numerator of one fraction and multiplying it by the denominator of the other fraction. So we're looking at the two numbers that are diagonal from each other. So for this cross product we have two times nine, which is 18. And for the other cross product, we'll look at the numbers on the other diagonal. Five times seven gives us 35. These cross products are not equal to each other, 18 is not equal to 35. So that tells us that the ratios are not proportional. Here's our last example. Determine whether seven over 20 is proportional to 21 over 35. And our third method for this one will be to convert the fractions to decimals. So here's our two fractions. And remember to convert a fraction to a decimal, we can divide the numerator by the denominator. So on the fraction on the left, we're going to do seven divided by 20, which gives us 0.35. And for the fraction on the right, we'll do 21 divided by 35 and that gives us 0.6. And we can see that these decimals are not equivalent. So therefore the ratios are not proportional. So you just learned three different methods that you can use to determine whether ratios are proportional to each other.