Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 1

(a) What is 72% as a fraction? Circle your answer. [A] 3/4 [B] 18/25 [C] 4/5 [D] 37/50. (b) What is 0.18 as a percentage? Circle your answer. [A] 180% [B] 18% [C] 1.8% [D] 0.18%

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Video Transcript

Part a) What is 72 percent as a fraction? Circle your answer. The options are three-quarters, 18 over 25, four-fifths, or 37 over 50 part. Part b) What is 0.18 as a percentage? Circle your answer. The options are 180 percent, 18 percent, 1.8 percent, or 0.18 percent.

Well for part a, there’s a couple of ways we can go about this. The first way is to take the 72 percent and convert it into a fraction, which is what I’m gonna do to show you this first method. The other way would be to convert each of our fractions in turn. Well, if we’ve got 72 percent — well, percent means out of 100. So therefore, 72 percent is gonna be 72 out of 100 or 72 over 100.

So now what we need to do is simplify our fraction. And to do this, we need to find a common factor between 72 and 100. Well, we could find the highest common factor, which is gonna be four in this case. But it might be easy to do by using a factor that you know. And you can work out easily. So in this case, we can see that both are even numbers, so therefore can both be divided by two. So if we divide 72 by two, we get 36. And if we divide 100 by two, we get 50.

If we wanted to work out how we do 72 divided by two, we could use the bus stop method. And two is going to seven three times, with one remainder. So we carry that. Then, we do twos in 12, which is six. So therefore, we get our 36, which is what we wanted. And then, 100 divided by two, the best way to do this is by thinking about it as 10 divided by two would be five. So therefore, 100 divided by two would be 50. Okay, great. Now can we simplify it further?

Well again, we notice that 36 and 50 are both even numbers. So therefore, they can both be divided by two again. And when we divide this by two, we’re gonna get 18 over 25. And that’s because 36 divided by two is 18. 50 divided by two is 25. Again, we could use the bus stop method if we wanted for the 36 divided by two. So we see how many twos go into three is one, with one remainder. So therefore, what we’d have is twos into 16 because we carry that one, which is eight. So we get our 18. So the answer would be 18 over 25.

So if we check our answers, we can see that it’s the second answer. So therefore, 72 percent as a fraction is 18 over 25. Well, I did say there’ll be another way to solve this problem. And that way would be to show what the fractions were as percentages. Well, we could see the first fraction would not be correct because three-quarters is one of the fractions that we should know because three-quarters is 75 percent. And if we think about how we’d know that, well we know that a quarter of 100 is 25. So therefore, 25 percent is one-quarter. So three-quarters is gonna be 75 percent. So this is not 72 percent.

So then, if we looked at our second fraction, 18 over 25, well the way that we’d find out what this is as a percentage is we’d convert the denominator to 100 because, as we said, a percent is out of 100. So 25 multiplied by four is 100. So then, we’d have to multiply the top by four as well, which will give us the answer of 72. So therefore, we get our 72 percent. And if we’re thinking, well how do we multiply 18 by four, we can do that using a mental method. You do four multiplied by 10, which is 40, four multiplied by eight, which is 32. Add them together and you get your 72. So this would’ve been the correct answer. And we could’ve stopped here. But we’ll just show what the other two fractions are as percentages anyway.

Well, four-fifths — if you think of this, what we’d have to do again is get the denominator to be 100. Well, five multiplied by two is ten. So therefore, five multiplied by 20 is 100. So then, we’d have to do the same to the numerator. So four multiplied by 20 is 80. So therefore, it’d be 80 percent. So this would be incorrect. And then, finally, for our final fraction — to convert 37 over 50 into a percent, well again, we want the denominator to be 100. So we’d just double the denominator. So we multiply it by two. So we do the same to the numerator, which will give us 74 percent. So again, this is gonna be the correct answer. Great! So we finished part a. Let’s move on to part b.

So in part b, what we want to do is find out what 0.18 is as a percentage. Well, to convert from a decimal to a percentage, we multiply by 100. And to convert from percentage back to a decimal, we divide by 100. Well therefore, what we’re gonna do is multiply our decimal by 100. So we’ve got 0.18. Now, if we multiply by 100, what it means here is that each of our digits moves two place values to the left. So therefore, our one would move from being a tenth to a ten. And our eight would go from the one hundredth column to the units column. So therefore, we’d have 18. So therefore, the correct answer would be 18 percent. So 0.18 as a percentage is 18 percent.

Now, we could double-check this by seeing what our other percentages would be as decimals. And we’ll do that by dividing by 100. Well, first of all, we’d have 180 percent. Well, if we divided 180 by 100, then what would happen is each five digits would move two place values to the right. So the one would instead of being 100 would be a unit. So we get 1.8 or 1.80. But we wouldn’t have to necessarily write the zero. So this wouldn’t be 0.18.

We’ve already ascertained that 18 percent would be 0.18. And if we think about it, if we moved two place values to the right, then the one would become instead of being a ten, it would be a tenth. And the eight would become instead of a unit a hundredth. So it gives us 0.18, which is what we want. 1.8 percent would be 0.018 because the one would go from a unit to a hundredth. And the eight would go from a tenth to a thousandth. And finally, 0.18 percent would be 0.0018.

So therefore, we’ve showed and checked that 18 percent is 0.18 as a percentage.

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