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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.
6.2

## National STEM Learning Centre

Skip to 0 minutes and 7 seconds PAULA KELLY: We’re going to have a look now at how to find a percentage of an amount. Two methods, we’re going to have a look at. One is in fractions and one with decimals. So we’re going to start off by finding 30% of 72. So with our fractions, we know percent, 30 parts of 100. “Of,” we know can substitute with multiply. I’m looking at 72. We’re using fractions, so we could put 72 whole ones. We know as well to find our answer, we multiply our numerators. So I know from a calculator that 30 times 72 is going to give me 2,160. I am quite happy with this one, though. We’ve got 100.

Skip to 0 minutes and 58 seconds PAULA KELLY: To make our final answer, then, if we’re dividing by 100, all our numbers go two places smaller. Our final answer is 21.6.

Skip to 1 minute and 8 seconds MICHAEL ANDERSON: So there’s quite a lot of big numbers in there. With the 30/100 and the 72/1, could we try to, maybe, cancel those down a little bit beforehand?

Skip to 1 minute and 17 seconds PAULA KELLY: Yeah, as we saw earlier, we definitely could simplify these. As we’re looking to put into a number answer rather than a fraction, keeping our denominators 100 lets us quite easily make it into a number.

Skip to 1 minute and 27 seconds MICHAEL ANDERSON: Oh, OK, I see, yeah.

Skip to 1 minute and 29 seconds PAULA KELLY: So our first method using a fraction, also we could use a decimal. We know 30%– 30 parts of 100, 30 divided by 100– is same as 0.3. “Of,” so we’re multiplying 72. As we saw earlier as well, this is a bit more tricky. We could use three lots of 72, so three 70s is 210. So actually, it’s 216. That’s our estimation.

Skip to 2 minutes and 4 seconds PAULA KELLY: We’ve made our answer 10 times bigger, really. So let’s get an answer back to the right scale. If this is 10 times smaller, our final answer is also 10 times smaller. So all our numbers go one place smaller. So again, we have 21.6. Both our answers match, so we’re pretty confident we’ve got it right.

# Finding a percentage of an amount recap

Before watching the video you may like to consider how you would calculate 30% of 72.

In this video we have a quick recap of how to find a percentage of an amount using fractions and a decimal multiplier. The recap uses a number of the techniques used in earlier parts of the course, including:

• Writing the percentage as a fraction then finding the appropriate fraction of 72.
• Writing the percentage as a decimal then multiplying the decimal by 72.
• Finding 10% or 1% of 72 by dividing by 10 or 100 then scaling up to find 30%.

## Problem worksheet

Now complete question 1 from this week’s worksheet.