Learn To Express Values as a Ration In this lesson, let’s learn about expressing values as ratios. We’ll do two problems. Let’s do the first one first. The problem says for us to express the following as simple ratios and to write them in three different forms. First part says 14 boys and 26 girls. We need to write 14 boys and 26 girls. We need to express that as a ratio. A ratio is a way of describing a relationship between the two. A ratio can be expressed as 14:26. There’s many different ways to write it. We can say 14 boys to 26 girls, that’s one way of writing it. The same ration can also be expressed in a couple of different ways. We could say 14:26 which is one way of doing it. We could also write it as 14 boys over 26 girls, either way. It’s 14 to 26, 14:26, 14/26; these are all different ways of writing the same ratio. Let’s do the other one. The second one is length of a rectangle is 15cm and its width is 8cm. The ratio is 154cm to 8 cm or 15:8 or 15/8. All of these are applicable ways of writing ratios. Let’s try the second problem. It says Alex plays two different games for 120 minutes a day. That’s exactly two hours a day. If he plays tennis for 50 minutes, what’s the ratio of the time spent playing tennis to the total time spent? We need to find the ratio of time spent playing tennis to total time. Let’s write down what we know. We know that the time spent on tennis is 50 minutes, total time spent playing is 120 minutes. That’s what we’re given. Out of the 120 minutes, he plays tennis for 15 minutes. So, let's take some more space. So, the ratio of time spent playing tennis over or to time spent playing in all, playing all sports or games equals 50 minutes/120 minutes. I can divide both of these by their greatest common factor. 50/120 is the ratio. Both of these share a greatest common factor 10. If I divide them, we get 5/12, that’s the ratio in simplest form. We can also write this ratio as 5:12 or 5 to 12. All of these would be correct. Quickly recapping what we’ve picked up. When we are given situations that we need to express as ratios, ratios express a relationship between many values, in this case two. If it’s 14 boys to 26 girls, the ratio is 14 to 26, 14:26, or 14/26. Again, I could have written this in simplest form by taking 14/26 dividing by 2 which is their greatest common factor which will give us 7/13. That’s the same ratio as well. Same thing with 15 is to 8, different forms, if we’re given problems where we know the person plays tennis for 15 minutes and he plays everything for 120 minutes, the ratio is 50/120 which I can divide by GCF to get it in simplest form. Other ways of writing it are given here as well.