Video: AQA GCSE Mathematics Higher Tier Pack 2 β€’ Paper 3 β€’ Question 4

Make π‘Ÿ the subject of the equation 𝑠 = (3𝑑)/(2π‘Ÿ). Circle your answer. [A] π‘Ÿ = (2𝑑)/(3𝑠) [B] π‘Ÿ = (3𝑑)/(2𝑠) [C] π‘Ÿ = (2𝑠)/(3𝑑) [D] π‘Ÿ = (3𝑠)/(2𝑑)

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Video Transcript

Make π‘Ÿ the subject of the equation 𝑠 is equal to three 𝑑 over two π‘Ÿ. Circle your answer. Is it π‘Ÿ is equal to two 𝑑 over three 𝑠, π‘Ÿ is equal to three 𝑑 over two 𝑠, π‘Ÿ is equal to two 𝑠 over three 𝑑, or π‘Ÿ is equal to three 𝑠 over two 𝑑?

It should be fairly obvious from the answers we’ve been given that to make π‘Ÿ the subject we’re looking for an equation which is π‘Ÿ 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 𝑑 over two π‘Ÿ. At the moment, this fraction is making things look a little bit nasty. So we’re going to multiply both sides by two π‘Ÿ. 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 π‘Ÿ gives us two π‘Ÿ 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 π‘Ÿπ‘ . Three 𝑑 divided by two π‘Ÿ and then multiply it by two π‘Ÿ is simply three 𝑑. To get π‘Ÿ to be the subject of this equation, we need to divide by two and 𝑠 since at the moment π‘Ÿ is being multiplied by both two and 𝑠.

Two π‘Ÿπ‘  divided by two 𝑠 is simply π‘Ÿ, and three 𝑑 divided by two 𝑠 is three 𝑑 over two 𝑠. And we can see that the correct answer is therefore π‘Ÿ is equal to three 𝑑 over two 𝑠. Now you might have noticed that we started by multiplying by two π‘Ÿ 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 π‘Ÿ. That’s π‘Ÿπ‘  is equal to three 𝑑 over two. Then we would divide both sides by 𝑠 to once again give us π‘Ÿ is equal to three 𝑑 over two 𝑠. Either method is absolutely fine. The answer is π‘Ÿ is equal to three 𝑑 over two 𝑠.

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