 This video is called ratios. What we're going to do is practice writing ratios and then reducing our answer to the lowest term. Ratios can be written in a number of ways. You can write them as a fraction, or you can write the two numbers with a colon in between them. I think we will stick with writing them as fractions because that will be the most helpful for us when we do our story problems in geometry. Very quickly, the statement we're going to be working with says, out of the 925 seniors, 405 are boys. Let's do some quick subtraction and see that if 405 are boys, then 520 must be girls. That will just help us with our problems A, B, and C. Alright, so problem A, the first one says, what is the ratio of boys to the total number of seniors? What's important in writing ratios is what order you put things in. Since boys was listed first, it would be written first if we were going to use a colon. So we would say 405 colon. And then so the ratio of boys to the total number of seniors. So total of number of seniors was listed second. So that would go after our colon of 925. If we were going to write it in fraction form, which is what I recommend you do for math class, we're going to have what's listed first, the boys. That will go in the numerator. And the total number of seniors of 925, since that was listed second, goes in the denominator. So that is a correct ratio, but I'm going to reduce it a little bit. Since both 405 and 925 end with a 5, I know I can divide both sides by 5. So I end up with 81 over 185. For my second example, what is the ratio of the total number of seniors to boys? Since seniors was listed first, that's what you would write first, 925. Then you write the colon and we're comparing it with boys. And there was 405 boys, so that would be written after the colon. If we were going to do it in fraction form, which is what I recommend for math class, we will do 925 because that was listed first over 405. Notice these are the same numbers as our first example. They are just written in a different order or put in a different spot because the ratio was different. It's all about the order it was listed to you in the problem. So here when I divide both sides by 5, I get 185 over 81. My last problem says what is the ratio of girls to boys? So in this case girls were listed first, so it would be that number will be put in the numerator. Boys was listed second, so that number will be put in the denominator. So girls 520, boys 405. So that would be a ratio, but I can definitely reduce this one as well. Since the numerator ends in a 0 and the denominator ends in a 5, I can divide both the top and the bottom by 5 and that will give me 104 over 81. So that would be my ratio written in reduced terms. Having this scale will be important starting now this chapter when we look at similar triangles. We will be looking at ratios and scale factors a lot and they will be written like this. So practice writing your ratios, make sure you understand what's listed first, goes in the numerator, what's listed second goes in the denominator.