Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 23

GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 23

05:44

Video Transcript

In a sale, a shop is temporarily reducing the price of a particular washing machine that normally costs 420 pounds by 13 percent. What will the sale price of the washing machine be?

There are a number of ways we can answer this question. We’ll look at methods that can be used for a non-calculator question such as this, first.

The starting price of the washing machine is 420 pounds. This means that 420 pounds is 100 percent of the original price. 100 divided by 10 is 10. So we can work out 10 percent of the original price by dividing it by 10.

Remember, to divide 420 by 10, we move all the digits to the right one place. The four moves from the hundreds to the tens. Then the two moves from the tens to the units column. Remember, the decimal points line up, and the zero moves from the units to the tenths. In fact, this zero was just a placeholder, so it doesn’t really matter whether we incorporate it or not. Had this been any other digit apart from zero though, it would have moved into the tenths column. That means then that 420 divided by 10 is 42 pounds. 10 percent of 420 is 42 pounds.

We want to work out 13 percent of the price, so we’ll next work out one percent of the original number. 10 divided by 10 is one, so we can divide 42 by 10 to work out one percent of 420. Once again, to divide by 10, we move all the digits to the right one place. 42 divided by 10 is 4.2. In money terms, one percent of 420 pounds is four pounds 20.

We could alternatively have worked out one percent by dividing the original number by 100. Either method is valid.

Now that we know the value of one percent, we can work out three percent by multiplying four pounds 20 by three. We could use repeated addition to do that. By lining up the decimal points carefully, we get that 4.20 multiplied by three is 12.60. In money terms, three percent of 420 pounds is 12 pounds 60.

Alternatively, we could have used a formal written method for multiplication, such as the column method. Remember, when multiplying a decimal number by an integer using the column method, we can add a decimal point in the answer directly below the decimal point in the question. Once again, that gives us a value of 12 pounds 60.

Next, to find 13 percent of 420 pounds, we’ll add the values for 10 percent and three percent. That’s 42 pounds plus 12 pounds 60. We could do that in our head, but it’s sensible to use the column method for addition to prevent making any mistakes. 42 pounds plus 12 pounds 60 is 54 pounds 60.

We do need to be a little bit careful. The price of the washing machine has been reduced, so it’s not enough to leave an answer as 54 pounds 60. We’ll need to subtract that from the original price of the washing machine. That’s 420 pounds minus 54 pounds 60.

This is quite a tricky calculation. So again, we’ll use the column method, this time for subtraction. Zero minus zero is zero. We don’t do zero minus six in the column method. Instead, we borrow a one from the first nonzero digit to the left. In this case, we borrow one from the two. The two becomes one, and the zero just to the right of it becomes 10. Then we borrow a one from that 10. That 10 becomes nine, and our zero then becomes 10. 10 take away six is four, and nine take away four is five. We don’t do one takeaway five. Instead, we borrow one from the four. The four becomes three, and our one becomes 11. 11 minus five is six, and three minus zero is three. We’ve worked out the sale price of the washing machine to be 365 pounds 40.

Now we said there was an alternative method. This method is slightly quicker, but it works better in a calculator exam. For this method, we use the fact that percent means out of 100, to write 13 percent as a fraction. 13 percent is equal to 13 out of 100. It’s thirteen one hundredths. We could leave it like this or we can convert it into decimal form.

Thirteen one hundredths is equivalent to 0.13. That might be something you know by heart. If not though, remember the fraction line means divide. We’re doing 13 divided by 100. And we’ve already seen that, to divide by 100, we move the digits to the right two places. That gives us 13 divided by 100 is 0.13. Then to work out 13 percent of 420, we’ll multiply 420 by either 0.13 or thirteen one hundredths. That gives us a value of 54 pounds 60. The sale price of the washing machine is 365 pounds 40.

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