Make 𝑟 the subject of the equation 𝑠 is equal to three 𝑡 over two 𝑟. Circle your answer. Is it 𝑟 is equal to two 𝑡 over three 𝑠, 𝑟 is equal to three 𝑡 over two 𝑠, 𝑟 is equal to two 𝑠 over three 𝑡, or 𝑟 is equal to three 𝑠 over two 𝑡?
It should be fairly obvious from the answers we’ve been given that to make 𝑟 the subject we’re looking for an equation which is 𝑟 is equal to some other expression. Just like we’re solving equations, to achieve this, we’re going to need to perform a series of inverse, that means opposite, operations.
Let’s start with 𝑠 is equal to three 𝑡 over two 𝑟. At the moment, this fraction is making things look a little bit nasty. So we’re going to multiply both sides by two 𝑟. Now this isn’t the only first step that we can take, and we’ll look at slightly different method in a moment. Multiplying both sides by two 𝑟 gives us two 𝑟 multiplied by 𝑠 on the left-hand side of this equation. Remember, we try to avoid using the multiplication symbol in algebra, so we just write two 𝑟𝑠. Three 𝑡 divided by two 𝑟 and then multiply it by two 𝑟 is simply three 𝑡. To get 𝑟 to be the subject of this equation, we need to divide by two and 𝑠 since at the moment 𝑟 is being multiplied by both two and 𝑠.
Two 𝑟𝑠 divided by two 𝑠 is simply 𝑟, and three 𝑡 divided by two 𝑠 is three 𝑡 over two 𝑠. And we can see that the correct answer is therefore 𝑟 is equal to three 𝑡 over two 𝑠. Now you might have noticed that we started by multiplying by two 𝑟 and then dividing by two 𝑠. Since multiplying by two and then dividing by two cancel each other out, we could have begun by multiplying both sides by 𝑟. That’s 𝑟𝑠 is equal to three 𝑡 over two. Then we would divide both sides by 𝑠 to once again give us 𝑟 is equal to three 𝑡 over two 𝑠. Either method is absolutely fine. The answer is 𝑟 is equal to three 𝑡 over two 𝑠.