Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 4

How many hours are there in 270 minutes? Circle your answer. [A] 4 [B] 4 1/2 [C] 5 [D] 4 1/4.


Video Transcript

How many hours are there in 270 minutes? Circle your answer. The options are four, four and a half, five, or four and a quarter.

So the first thing we need to know of this problem is the fact that one hour is equal to 60 minutes. And we’re gonna use this to help us solve the problem. So therefore, what we want to find out is how many 60s go into 270. And that’s because that will tell us how many hours there are in 270 minutes. The way that we find out how many 60s go into 270 is by using division as the operation. So we’ve got 270 divided by 60. I’ve written it as 270 over 60 cause this means the same thing. But it’ll help us when we’re doing the division.

Well, first of all, before we have to calculate anything, what we can do is we can divide the numerator and denominator by 10. So therefore, in practical terms, this means that we can cross off a zero from both. So now, we have 27 over six. So now, what we do is we look for a common factor. Well, a common factor of both 27 and six is three. Well, when we work this out, we get nine over two because we divide the numerator by three. So 27 divided by three is nine. And we divide the denominator by three. So six divided by three is two. But is this any of our answers? Well no, it isn’t. So what can we do?

Well, we’ve got a top heavy or improper fraction. What we need to do is convert it into a mixed number. And to do that, first we’ll see how many twos go into nine. Well, four twos go into nine. And that’s because four multiplied by two is eight. And that means we’ve got one remainder. So therefore, we can have one. And this is over two because we already had two as the denominator. So therefore, we can say that there are four and a half hours in 270 minutes. So therefore, we could circle the second answer, which will be correct.

And we can check this answer by using another method, which would be counting up. So if we start with 60 and we add 60, well this is the same as six add six, which is 12, then we’ve got a zero on the end. So it’s gonna be 120. So that’s two hours. So we haven’t reached our 270 yet. So we’re gonna add another 60, which takes us to 180. So that’s three hours. We still haven’t got to 270 yet. So then, we add another 60, which gets us to 240. So that’s four hours. So we still haven’t got to 270 minutes. But it also means that we can rule out four hours. Well, if we add another 60 to make five hours, this gets us to 300. Well, 300 is too big cause it’s greater than 270 minutes. So we can rule out five hours as well. So we know it’s gonna be four hours. But we’ve got some left over.

So we need to work out how much that is. So we do 270 minus 240, which I’ll set up here in a column subtraction. So we have zero minus zero, which is zero, seven minus four, which is three, and two minus two, which is zero. So we’ve got 30 left over. Well, as 30 is half of 60 and therefore 270 minutes is gonna be equal to four and a half hours, which is the same answer as we got in the first method.

So therefore, we can definitely say that 270 minutes is equal to four and a half hours.

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