Learn about Equivalent Ratios Equivalent ratios, so on this problem, we need to find two ratios equivalent to 3:5. Now, equivalent ratios can be represented by equivalent fractions. All right, so to find the two ratios equivalent to 3:5 we need to follow these steps. Our first step is we need to express the ratio as a fraction, so we need to express the ration as a fraction, so 3:5 would be written as such 3/5. Now, out second step is to multiply the numerator and the denominator by the same number except we cannot use zero or 1. So let’s multiply the numerator and the denominator by two. So we’re going to multiply by 2. So I’m going to take 3/5 and I’m going to multiply both by 2 and I get 6/10. So 6/10 can also be written as 6:10. Now, let’s multiply the numerator and the denominator by three. So let’s take our original problem and multiply each by 3. And then we get 9/15th which could be written as such, so two equivalent ratios to 3:5 are 6:10 and 9:15. Let’s move on to your second problem. Here we need to determine whether 1:2 and 3:6 are equivalent. So here we’re talking about proportion. So proportion indicates that two ratios are equivalent or that they’re equal to each other. So equivalent means equal to each other, so we can use cross product to see if the ratio is equivalent, so to find the proportion we can use cross product. To find the cross product we multiply the numerator of one fraction by the denominator of the other fraction. So we take the numerator or let’s say fraction A and the denominator of fraction B. So we take the numerator of one fraction and multiply it by the denominator of another fraction and then repeating the process for the other numerator and denominator. So let’s determine if 1:2 and 3:6 are equivalent, if they’re the same. So what we’re going to do is first we need to express our ratios into fractions, as fractions. We’re going to take 1:2 and put it as a fraction and then we’re going to take 3:6 and put it as a fraction. Now, we need to find the cross product. So our next step is to find the cross product. So again, to find the cross product we’re going to find them as such and then I’m going to multiply. So I’m going to multiply the 6 and the 1, the numerator of one fraction and the denominator of the other fraction and then the denominator of this fraction with the numerator of the other. So do the opposite. So we have 1 x 6 equals 3 x 2. So then we get 6 = 6. So the cross products are the same, so that means when the cross products are the same the ratio is equivalent. We can also compare the ratio by using the least common denominator. So let’s find and compare the ratios using the least common denominator. So we need to compare 1:2 and 3:6. The first step we’re going to do is we’re going to express the ratio as a fraction, so 1:2 is 1/2 and 3:6 is 3/6. Now, we need to rewrite the fraction with that lowest common denominator. So we need to rewrite with the lowest common denominator. So least common denominator is the least common multiple of the denominator, so we need to find the least common multiple of both the denominators. So we need to find the least common multiple of 2 and 6. So multiply the numerator and denominator of one half by three, so we’re going to multiply 1/2 x 3/3 and 3 and 6 by 1 because the lowest common multiple of 2 and 6 is 6, so we know that the lowest common multiple is six so we know that 2 x 3 is 6so that’s why we’re going to multiply 1/2 x 3 and then we’re going to multiply 3/6 x 1 because 6 x 1 is 6, that would give us the lowest common multiple. So when we do that we get 3/6 and 3/6, so when I compare 3/6 is equal to 3/6, since both of the fractions are same the fractions are equivalent. All right, things to remember and to keep in mind is that equivalent ratios can be represented by equivalent fractions. Two ratios that are equivalent they are proportionate, and we can use cross product to see if the ratios are equivalent. To find a cross product we f