Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 3 • Question 2

What is 120 as a percentage of 30? Circle your answer. [A] 40% [B] 25% [C] 360% [D] 400%


Video Transcript

What is 120 as a percentage of 30? Circle your answer. Is it 40 percent, 25 percent, 360 percent, or 400 percent?

We need to write 120 as a percentage of 30. It can be sensible to begin by actually writing this as a fraction. 120 out of 30 is the same as one hundred twenty thirtieths as shown. And there are two ways we can convert a fraction into a percentage.

The first method is to find an equivalent fraction whose denominator is 100. To do that, we’ll need to figure out what we can multiply 30 by to get 100. And in fact, that’s not a particularly easy calculation. So we’ll introduce a middle step. Instead, we’ll divide both the numerator and the denominator by three. And the reason we do this is because it makes the denominator 10, which is a factor of 100. 120 divided by three is 40. So 120 over 30 is the same as 40 over 10. And since 10 is a factor of 100, we can multiply it by 10. And the denominator becomes 100.

Let’s do the same to the numerator. 40 multiplied by 10 is 400. So 120 as a fraction of 30 is equivalent to 400 over 100. And since percent means out of 100, we can say that 400 over 100 is the same as 400 percent.

And I said there was a second method. This method works nicely in a calculator paper. And we can change a fraction and a decimal into a percentage by multiplying it simply by 100. If we had calculated one hundred twenty thirtieths multiplied by 100, we once again would’ve got 400. So as a percentage of 30, 120 is 400 percent.

And if we look at the other answers, we can see that we could have eliminated two of them straight away. 120 is a much larger number than 30. It therefore would make no sense that 120 would be 40 percent or 25 percent of 30. We know that it’s larger than the original number. It’s larger than 100 percent. So it would’ve had to have been either 360 percent or 400 percent. Of course, we’ve shown it’s 400 percent.

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