## Want to keep learning?

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.
6.8

## National STEM Learning Centre

Skip to 0 minutes and 8 seconds PAULA KELLY: So now we’re going to see how we can calculate profit as a percentage. So for example, a garage buys a car for 5,200 pounds. They sell that car for 6,000 pounds. So we know they’ve made a profit of 800 pounds, but what’s that as a percentage? So how could we do this?

Skip to 0 minutes and 27 seconds MICHAEL ANDERSON: OK, well, we need to know the profit that they’ve made. So in this case, it was 800 pounds. We’re going to divide that by the original amount. So in this case, it was how much they paid for the car in the first place. And that was 5,200. So I’m going to write that as a fraction, 800 over 5,200. And then we’re going to try and simplify this a little bit. I suppose I could divide them both by 100, so I’d get 8 over 52. But to be honest, I’d probably just do this with a calculator. 8 divided by 52, and then, hopefully, our calculator would give you an answer of 0.153846, dot, dot, dot.

Skip to 1 minute and 6 seconds So that’s an answer as a decimal. But obviously, we wanted it as a percentage. So we could say 15.38% or something like that. But to the nearest whole percentage is 15%. So they made a 15% profit on this car.

Skip to 1 minute and 22 seconds PAULA KELLY: OK, so we’ve seen one method of working that out. Is there another method we could use?

Skip to 1 minute and 27 seconds MICHAEL ANDERSON: Yeah. So we’ve seen the idea of a multiplier being used. Our original amount was 5,200. And we ended up with 6,000 pounds that we sold the car for. Now, in order to get from 5,200 to 6,000, we can multiply by a multiplier. So let’s multiply it by some number and call it M. Now, in order to figure out what the multiplier is, I’m going to have to divide both sides by 5,200. And by doing that, the M stays there. I end up with 6,000 divided by 5,200. Now, I could try and simplify this and calculate it down using fractions. But to be honest, I’m just going to pop this into my calculator.

Skip to 2 minutes and 10 seconds And it’s going to give me a value of 1.153846 dot, dot, dot.

Skip to 2 minutes and 16 seconds PAULA KELLY: So what’s that value actually tell us now then?

Skip to 2 minutes and 19 seconds MICHAEL ANDERSON: Well, if you think about the previous example, we actually got 0.153846. And this 1–

Skip to 2 minutes and 25 seconds MICHAEL ANDERSON: Yeah, it’s really similar. But this 1 represents the original amount, as well. So if we just look at the decimal part, well, that’s 0.1538. So that’s going to basically tell us that the profit, on top of actually the amount that we pay, the 5,200, is 15%. So they’ve made a 15% profit.

# Finding a percentage increase

In this video we consider two similar methods of finding a percentage increase. Percentage increases, or decreases, are used to allow comparisons of different amounts in many situations, for example profit and loss, or change in exam performance.

When finding a percentage increase we are asking the question: “by what percentage we have to increase the original amount by to find the new amount?”

The first method uses the equation:

$\frac{profit}{original\ amount} \times 100$

It is important, when using this method, to explore what the equation means and from where it originates.

The second method uses a multiplier, M, with the equation:

$original\ amount \times M = new\ amount$

The answer then has to be interpreted correctly. If M is greater than 1, it tells us that it is a percentage increase.

The decimal part, after ‘1’, indicates the magnitude of the percentage increase. For example, a value of M of 1.15 indicates a 15% increase.

## Question

If the multiplier was found to equal 2 what would that mean? If you think the multiplier can never equal 2 explain why. If you think it can give an example.

What would a multiplier of 2.5 tell us? Post your thoughts in the comments below.

## Problem worksheet

Now complete questions 9, 10 and 11 from this week’s worksheet.