Video: GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 11

GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 11

04:22

Video Transcript

Part a) Calculate 13 multiplied by nine. Part b) Calculate 84 divided by six. And part c) calculate the cube root of negative eight.

So to work out part a, there’s actually a couple of methods we can use. So we can do the calculation 13 multiplied by nine in a couple of different ways. So the first method, method one, what we do first is actually leave 13 multiplied by 10. And we’re gonna do that because actually the original calculation is 13 multiplied by nine which is actually very close to 13 multiplied by 10. And we actually deal with something afterwards to actually give us the correct answer.

We do 13 multiplied by 10 because it’s an easy calculation as we know that 13 multiplied by 10 is 130. And we’ve done that because we’ve actually added a zero onto 13. Okay, great, but how does this help us? Well, it helps us understand a good way to think about it is like this: 13 multiplied by nine is nine lots of 13, 13 multiplied by 10 is 10 lots of 13. In that case, if we have 10 lots of 13 and we take away one lot of 13, then we’ll have nine lots of 13 which is what we’re looking for.

So therefore, what we can do is have 130 because that’s our 10 lots of 13 and then we take away or subtract 13 because that’s one lot of 13. So we get 117. And that’s gonna be our answer. We got that because if you take 10 away from 130, 120. Then, take another three gives us 117. Okay, great, so that’s the answer cause we know that’s nine lots of 13.

Right, let’s have a look at our second method. Well, the second method is by using column multiplication. So I’ve set it up here. We’ve 13 multiplied by nine.

So first of all, we do nine multiplied by three which gives us 27. So we put seven in the units column and then carry the two. And then, we do nine multiplied by one, well nine multiplied by 10 because it’s the one from the 13 which gives us nine or 90 add the two we carried gives 110 or 11. So therefore, we’re gonna put one into the tens column and one into the hundreds column, yet again, getting our answer of 117.

Okay, great, part a dealt with, let’s move on part b. Now, to complete part b, what we need to do is divide 84 by six. And in order to do that, what we’re gonna do is use short division or the bus stop method. So I’ve set it up here.

So first of all, what we do is see how many sixes are going into eight. And it goes into eight once with a remainder of two. So we carry the two. So now, we’ve got 24. And what we want to do is see how many sixes are going to 24. Well, six goes in 24 four times. So therefore, we have our answer of 14. So we can say that 84 divided by six is equal to 14.

Brilliant! Now, let’s move on to part c. Well, for part c, what we need to do is calculate the cube root of negative eight. But first of all, we want to think about well, what’s the cube root of eight. Well, the cube root of eight is equal to two. And that’s because two multiplied by two is four multiplied by two gives us eight. And actually, it’s a good idea to actually remember the cube root of eight, the cube root of 64, and the cube root of 125 cause these are quite common.

Okay, so we’ve got that. However, there’s something a little bit different in the calculation that we have in the question. We can see that there’s a negative sign. Does this make any difference? Well, the answer is yes, because the cube root of negative eight is negative two.

And the reason for this is because actually negative two multiplied by negative two multiplied by negative two gives us four multiplied by negative two. And that’s because negative two multiplied by negative two is four because a negative multiplied by a negative is a positive. And if we got four multiplied by negative two, well, four multiplied by two is eight. But a positive multiplied by a negative is a negative. So we get the result negative eight.

So therefore, we can say that the answer to the calculation the cube root of negative eight is negative two.

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