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.
6.5

National STEM Learning Centre

Skip to 0 minutes and 7 seconds MICHAEL ANDERSON: So let’s take a look at decreasing an amount by a percentage. In a shop, a dress is worth 65 pounds, but in the sale is reduced by 15%. How would we work this out?

Skip to 0 minutes and 18 seconds PAULA KELLY: There’s a couple of ways of doing it. So we’re saying the dress was 65 pounds. And we’re reducing that by 15%. OK, so we could use our fractions or our decimals. We’ll find the 15%, and then we’ll take off our cost. So fractions first. If we had our 65 pounds and our 15%, we’ve got 15% out of 100 at 65 pounds is a whole number– so fraction over 1. We could do 15 times 65.

Skip to 0 minutes and 53 seconds MICHAEL ANDERSON: Without a calculator, that seems pretty tricky.

Skip to 0 minutes and 57 seconds PAULA KELLY: So instead, if we just simplify– these are both multiples of 5. So we’ve got 20 in there, 13 there. Still quite big.

Skip to 1 minute and 6 seconds MICHAEL ANDERSON: Yeah. Well, 15 and 20 are both multiples of 5, so we could divide them both by 5 as well.

Skip to 1 minute and 10 seconds PAULA KELLY: Lovely. [INTERPOSING VOICES]

Skip to 1 minute and 12 seconds PAULA KELLY: So got four 5’s in there, three in there. Much more manageable now.

Skip to 1 minute and 19 seconds PAULA KELLY: So we have 39 and 4. We wouldn’t necessarily [INAUDIBLE] this fraction.

Skip to 1 minute and 28 seconds MICHAEL ANDERSON: No. I suppose looking at it, though, 39’s close to 40, so it’s going to be just less than 10 pounds?

Skip to 1 minute and 34 seconds PAULA KELLY: Yep, so good to have what you’re aiming for– about 10 pounds. And you might just have a mixed number. So how many 4’s in 39?

Skip to 1 minute and 43 seconds MICHAEL ANDERSON: Well, nine 4’s are 36.

Skip to 1 minute and 46 seconds PAULA KELLY: Very good. Three are left over.

Skip to 1 minute and 48 seconds MICHAEL ANDERSON: To get to the 39, yep.

Skip to 1 minute and 50 seconds PAULA KELLY: Again, money isn’t generally done with fractions. We’ll write it as a decimal. So you’ve got 9.75.

Skip to 1 minute and 59 seconds MICHAEL ANDERSON: So is that the cost of the dress now?

Skip to 2 minutes and 1 second PAULA KELLY: Nope, that’d be a very good deal. I’m going to save 9.75.

Skip to 2 minutes and 5 seconds PAULA KELLY: So we’ll take off our original cost. So originally the dress was 65 pounds. We’ll take off our savings, our 15%, our 9.75. So if we take off 10, add on 25–

Skip to 2 minutes and 18 seconds MICHAEL ANDERSON: Right, OK. Nice trick, yeah. So take off 10 pounds, there’s 55, but then add on 25p, so 55.25.

Skip to 2 minutes and 27 seconds PAULA KELLY: Fantastic. Lovely. OK, so we’re going to pay that for our dress. So quite a nice method to do if you haven’t got a calculator, you’re doing a written method. If you did have a calculator, use some decimals. So we’ve got our 15% again– say percent out of 100. We divide it by 100 to get our decimal. So 0.15 of our original amount, so multiplied by 65.

Skip to 2 minutes and 52 seconds MICHAEL ANDERSON: I definitely need a calculator for this one.

Skip to 2 minutes and 55 seconds PAULA KELLY: Let’s use a calculator. Hopefully it will give us, again, 9.75. And then again, let’s take off our original cost–

Skip to 3 minutes and 3 seconds MICHAEL ANDERSON: To get 55.

Skip to 3 minutes and 4 seconds PAULA KELLY: Fantastic. So our original cost would take off what we’re saving. Same again. We’ll end up paying pur 55 pounds and 25 cents.

Skip to 3 minutes and 15 seconds MICHAEL ANDERSON: So which method, then– the fractions or the decimals– do you think is best?

Skip to 3 minutes and 20 seconds PAULA KELLY: Decimal’s quicker, definitely, if you had a calculator.

Skip to 3 minutes and 24 seconds PAULA KELLY: If not, we’d use this.

Skip to 3 minutes and 39 seconds So previously, we’ve seen a possibly more efficient method– using the multiplier. Can we use a multiplier when we’re decreasing by a percentage of amount?

Skip to 3 minutes and 47 seconds PAULA KELLY: Yeah, just the same– so as before we added on some percentage. Because you’re saving some percentage here, we can take that away. So rather than pay 100% of the cost of the dress–

Skip to 3 minutes and 58 seconds MICHAEL ANDERSON: Which was 65 pounds, yeah?

Skip to 4 minutes and 0 seconds PAULA KELLY: You’re saving 15%, so you’re only paying for 85%.

Skip to 4 minutes and 5 seconds MICHAEL ANDERSON: Ah, because 100 takeaway 15 gives us that 85?

Skip to 4 minutes and 8 seconds PAULA KELLY: Perfect, yeah. So just a bit more efficiently, we could say we’re going to pay for 85%. As a decimal, we divide it by 100– so 0.85. And it’s off the original price, so of 65. And all in one step, that would take off 15%, get us straight to the cost of the dress, that’s actually 55.25.

Skip to 4 minutes and 33 seconds MICHAEL ANDERSON: OK, so there’s no second step? We don’t have to take anything away? If we know that we’re going to pay 85%, we just work out 85% and find the total cost of the dress in the sale.

Skip to 4 minutes and 45 seconds MICHAEL ANDERSON: So with these percentage decrease questions, we can also think about it as a proportional reasoning question.

Skip to 4 minutes and 51 seconds PAULA KELLY: Yep, absolutely. So we could say we had our 100% was our 65 pounds.

Skip to 5 minutes and 1 second PAULA KELLY: And we’ll have those in boxes.

Skip to 5 minutes and 5 seconds You want to come down to our 85%.

Skip to 5 minutes and 7 seconds MICHAEL ANDERSON: Which is what we’re going to pay after the 15% has been taken off.

Skip to 5 minutes and 12 seconds PAULA KELLY: Perfect. So to get to our 100 to our 85, we’re going to multiply by 0.85.

Skip to 5 minutes and 20 seconds MICHAEL ANDERSON: Right, OK, yeah.

Skip to 5 minutes and 22 seconds PAULA KELLY: And if we lay it out like this, we can just see how they’re both exactly the same. So we’ve got multiplied, again, by 0.85. That’s going to give us our 55 pounds and 25 cents.

Skip to 5 minutes and 36 seconds MICHAEL ANDERSON: All right. So if it was a different amount– so if it went from 100% to, say, 80% that you’re going to pay– a 20% sale price– we’d multiply by not 0.8, or not 0.80, and do the same here?

Skip to 5 minutes and 52 seconds MICHAEL ANDERSON: Let’s have a look at an example for you to have a go yourself. A jacket is worth 135 pounds, but is reduced by 8% in the sale. How much would you now pay for the jacket? Pause the video to have a go yourself, and we’ll work through the solution in a moment.

Skip to 6 minutes and 13 seconds OK, so how would you work this one out?

Skip to 6 minutes and 15 seconds PAULA KELLY: So, again lots methods. My preferred method– with a calculator– would be using a decimal multiplier.

Skip to 6 minutes and 21 seconds MICHAEL ANDERSON: Right, OK, yeah.

Skip to 6 minutes and 23 seconds PAULA KELLY: So we have the jacket was 135 pounds, and we’re saving 8%. OK, so we are saving 8%. We’re going to pay 92%.

Skip to 6 minutes and 35 seconds MICHAEL ANDERSON: OK, yep, that makes sense.

Skip to 6 minutes and 36 seconds PAULA KELLY: So percent– parts of 100. We divide 92 by 100. We’re finding it of 135 pounds, so we’d multiply it by 135. Again, I would use a calculator. It’s going to end up costing 124.20.

Skip to 6 minutes and 55 seconds MICHAEL ANDERSON: Oh, nice. So is that the preferred method in this case?

Skip to 7 minutes and 0 seconds PAULA KELLY: I would do this with a calculator. It’s quicker. It’s just one step, you have a final answer. However, it might be easier to have fractions if no calculator. It’s entirely your choice, same answer.

Decreasing by an amount

The methods for decreasing an amount by a percentage are adaptations of the previous methods for increasing by a percentage. Before watching the video you may like to consider how you would approach the following two questions:

• Decrease 65 by 15%
• Decrease 135 by 8%

In this video Paula and Michael consider two different methods to decrease an amount by a percentage. Whilst the first, two-stage, method is simple to explain, the more efficient one stage ‘multiplier’ method is more useful when considering more challenging problems.

Problem worksheet

Now complete questions 2 to 5 from this week’s worksheet.
As a reminder, the worksheet is available from the first step of this week.