Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 7

GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 7

03:26

Video Transcript

Find three-fifths of 80.

So what we’re gonna do to be able to solve this problem I’m gonna show you two methods. First of all, let’s have a look at three-fifths of 80, what does it mean. Well, it actually means three-fifths times 80.

Now for the first method, what we can do is write it as 80 multiplied by three-fifths. So what we’re gonna do is we split it up. We split it up into 80 multiplied by three multiplied by a fifth. And the reason we can do that is because, actually, three multiplied by a fifth or three multiplied by one over five is gonna be equal to three-fifths or three over five. And that’s because if you have a fifth and then you multiply it by three and have three of them, it will give you three-fifths.

Well, if we look at the first bit of the calculation first, we’ve got 80 multiplied by three, or eight threes are 24, and then we add on the zero, so we get 240. And then this is multiplied by a fifth, which is gonna give us 48. And we get 48 because 240 multiplied by a fifth would give us 240, because I actually multiplied 240 by the one, because that was the numerator, over five. And then we can actually work this out by either dividing 240 by five or with this method I’m about to show you now.

Well, to make life easier, what we could do is actually multiply the numerator and denominator by two. And that’s just gonna make the denominator 10. And this will give us 480 over 10. And then we divide the numerator and denominator by 10, and we’re left with 48 over one, which is 48. So therefore, we can say that three-fifths of 80 is equal to 48. Okay, so that’s the first method.

Now I said I’ll show you another method. And I actually think the second method I’m about to show you some people do find a bit easier. But as with everything, it’s personal preference, and that’s why we show both methods so you can decide which one you would like to use.

So now for the second method, if we’re asked to find three-fifths of 80, now to find one-fifth of 80, which is what I want to do first, we actually divide 80 by five, which is going to be equal to 16. And we could’ve worked that out using the bus stop method for division.

So we do fives into eight. This goes once, remainder three. So I’m gonna carry the three, and then we do fives into 30, which is six. So therefore, we get 16. Okay, great! So that’s one-fifth. So what we did is we divided 80 by five. So now what do we do?

Well, now what we’re gonna do is find three-fifths. And to do that, we do 16 multiplied by three, which is going to be equal to 48 again. And to show you how we work this out, we could use column multiplication.

So first of all, we have three multiplied by six, which gives us 18. So we put eight in the units column, carry the one into the tens column. And then we have three multiplied by one, which is three. Then add the one that we had that we carried from earlier gives us four. So we get 48. So there we’ve got it, the same answer in both methods.

And just to recap the second method, so to find three-fifths of 80, what we did was we divided by the denominator, by five, to give us one-fifth, which was 16. Then we multiplied by the numerator, which was three, to give us 48. So therefore, we can say that three-fifths of 80 is equal to 48.