6.5

## National STEM Learning Centre

Skip to 0 minutes and 7 secondsMICHAEL 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 secondsPAULA 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 secondsMICHAEL ANDERSON: Without a calculator, that seems pretty tricky.

Skip to 0 minutes and 57 secondsPAULA 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 secondsMICHAEL 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 12 secondsPAULA KELLY: So got four 5's in there, three in there. Much more manageable now.

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

Skip to 1 minute and 28 secondsMICHAEL 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 secondsPAULA 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 secondsMICHAEL ANDERSON: Well, nine 4's are 36.

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

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

Skip to 1 minute and 50 secondsPAULA 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 secondsMICHAEL ANDERSON: So is that the cost of the dress now?

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

Skip to 2 minutes and 5 secondsPAULA 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 secondsMICHAEL 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 secondsPAULA 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 secondsMICHAEL ANDERSON: I definitely need a calculator for this one.

Skip to 2 minutes and 55 secondsPAULA 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 4 secondsPAULA 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 secondsMICHAEL ANDERSON: So which method, then-- the fractions or the decimals-- do you think is best?

Skip to 3 minutes and 24 secondsPAULA KELLY: If not, we'd use this.

Skip to 3 minutes and 39 secondsSo 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 secondsPAULA 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 secondsMICHAEL ANDERSON: Which was 65 pounds, yeah?

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

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

Skip to 4 minutes and 8 secondsPAULA 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 secondsMICHAEL 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 secondsMICHAEL ANDERSON: So with these percentage decrease questions, we can also think about it as a proportional reasoning question.

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

Skip to 5 minutes and 1 secondPAULA KELLY: And we'll have those in boxes.

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

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

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

Skip to 5 minutes and 22 secondsPAULA 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 secondsMICHAEL 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 secondsMICHAEL 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 secondsOK, so how would you work this one out?

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

Skip to 6 minutes and 23 secondsPAULA 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 secondsMICHAEL ANDERSON: OK, yep, that makes sense.

Skip to 6 minutes and 36 secondsPAULA 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 secondsMICHAEL ANDERSON: Oh, nice. So is that the preferred method in this case?

Skip to 7 minutes and 0 secondsPAULA 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.