Hello, welcome to Teach Me Raps. My name is Jonathan Hicks and we're discussing proportionality today. There are two kinds of proportionality: directly proportional and inversely proportional. If you say that one thing is proportional to another, it means they are directly proportional. So, you don't need to use the word "directly." However, sometimes we use it to distinguish it from inversely proportional. Let me give you examples of each type of proportionality. In the case of direct proportionality, let's imagine you have a job where you get paid £5 per hour. Your total pay, which we'll call P, would be the £5 per hour multiplied by the number of hours you work, which we'll call H. For example, if you worked for 3 hours, your pay (P) would be 5 times 3, which is 15. But if you worked for 6 hours, your pay would be 5 pounds times 6 hours, which is 30 pounds. In direct proportion, if the number of hours doubles, the pay doubles as well. So, if you work twice as long, you should get paid twice as much. This relationship is called proportionality. In contrast, let's discuss inverse proportionality. Imagine you have to mow a large lawn, like Buckingham Palace. It requires more than one person to mow the lawn; let's call the number of people mowing the lawn "N." The time it takes to mow the lawn, labeled "T," is inversely proportional to the number of people. In this case, we'll use a formula where T is equal to 8 divided by N. For example, if two people mow the lawn, T would be 8 divided by 2, which is 4. But if we double the number of people to four, T would be 8 divided by 4, which is 2. As you can see,...