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This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Fractions, Decimals, and Percentages. Join the course to learn more.
3.11

## National STEM Learning Centre

Skip to 0 minutes and 7 seconds MICHAEL ANDERSON: In the previous step, we asked you a series of percentage questions, which seemed at first relatively tricky. So one example was 36% of 50. Now hopefully, you got an answer to this of 18. But I’m going to consider a slightly different question instead, 50% of 36. Now, 50% is just a half, and half of 36 equals 18. It’s the same amount. So by changing the percentage sign from 36 to the 50, we seem to have got the exact same answer. And actually, this is a method, a strategy that’s going to work no matter what the questions are. If we think of our 36%, well, 36% means 36 out of 100, and we’re multiplying that by 50.

Skip to 0 minutes and 58 seconds Now, we’ve seen before that 50 can be written as a fraction 50/1, and then we’re just multiplying the tops and the bottoms together. We have 36 multiplied by 50 on the top, and on the bottom, 100 multiplied by 1. Now, multiplication is commutative, which means that the order in which we do these things doesn’t matter. So I could just as simply have 50 as the first number, multiply it by 36, and keep the bottoms in the same place– 100 multiplied by 1– which is the same question as 50% multiplied or 50% of 36, which is always going to give us our answer of 18. So let’s have a look at another example.

Skip to 1 minute and 38 seconds We could be asked to find something like 48% of 25. Now, finding 48% of 25 seems pretty tricky here, so what I’m going to do is, in fact, find 25% of 48 instead.

Skip to 1 minute and 54 seconds PAULA KELLY: That’s much nicer.

Skip to 1 minute and 55 seconds MICHAEL ANDERSON: Yeah, because 25% is a quarter. I can find a quarter of 48 relatively easily. Divide it by 4 and I get 12. So the answer to this one– 25% of 48– is 12, which means that 48% of 25 is also going to be 12.

# Finding a percentage of an amount: further examples

How would you calculate 36% of 50 or 48% of 25 without the aid of a calculator?

In this video, we see that having a clear understanding of how methods for finding a percentage of an amount enables learners to use this understanding to make a seemingly difficult calculation very easy. The main point to remember is that multiplication is commutative, in that you can do multiplication in any order.

## Teaching resource

An excellent teaching resource can be found on the STEM Learning website in the Inquiry Maths collection of resources. The resource is called 40% of 70 = 70% of 40.