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

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

04:03

Video Transcript

Shown are four numbers. Three, negative three, eight, negative eight. Use two of these numbers to finish the calculation. Something plus something equals negative five.

So looking at the numbers, straightaway, we can actually rule out two pairs of numbers. And we can do that if we actually just consider the five in the answer. So we disregard the negative and just look at the five.

We want the two numbers when actually added together to give us an answer that has a five in it. So therefore, we cannot have the two pairs of numbers that are three and negative three or eight and negative eight. And that’s because neither of these will actually give us a result that involves a five. Okay, so that’s great. We’ve ruled out two pairs.

Now, let’s see what other pairs are available. Well, the other pairs that are actually available to us are these four here. Remember that actually when it’s addition, we can actually have it either way around; it won’t affect it. We have three add eight, three add negative eight, negative three add eight, or negative three add negative eight.

Well, straightaway, we can actually rule out three add eight. Well, it’s gonna be 11. So we know that that can’t be right because it won’t give us negative five. But we could also rule it out straightaway because if we think of it that if we’ve got a positive add a positive, then therefore our answer is gonna be positive. But we need our answer to be negative because it’s negative five.

Okay, so let’s take a look at the other three pairs that we’ve got. So next, we have three add negative eight. Well, the first thing to note about three add negative eight is that when we actually have a plus and then a minus, then therefore what it actually become is a negative. So it actually become three minus eight.

So now that we know that the sum is gonna be three minus eight, let’s think about what this will look like on our number line. So we know we’re going left on our number line. And that’s because if you’re subtracting one positive number from another, then we know that we’re gonna go left on our number line. So we can see if we actually subtract eight from three, then we go down eight spaces.

So when we do that, what we’re gonna do is get to negative five, which is what we’re looking forward. So this is looking promising. So we can say that three add negative eight is equal to negative five and just to remind you it’s because three add negative eight turns into three subtract eight.

Okay, great, let’s move on to the next couple just to double check. So now, we’re actually gonna stop on negative three. And if we’re gonna add on eight, we’re gonna move eight spaces to the right. And when we do that, we’re gonna get to positive five. So therefore, we can say that negative three add eight is gonna be equal to five. So this is incorrect cause this is not what we’re looking for.

Okay, finally, we move on to our last pair. So now, for the last pair, we have negative three add negative eight. And as the same as the one previously, we know that if we’re gonna add a negative, it’s the same as subtracting the value. So it’s gonna be negative three minus eight. And therefore, as it’s negative three and minus eight, we’re gonna move eight spaces to the left. So we go from negative three, count eight spaces, and we get to negative 11, which again isn’t the value we’re looking for.

Okay, great, so we now know that the pair of our numbers is definitely gonna be three and negative eight. And we can just double check that cause we’ve already shown that three add negative eight is equal to negative five. Well, as we’re dealing with addition, it shouldn’t matter which way around it is. But we just double check. We’ve got negative eight add three.

So therefore, as we’re adding on three, we’re gonna be moving to the right. We can see if you move three places to the right, we get to negative five. So therefore, we can definitely say that if there are four numbers, three, negative three, eight, and negative eight, and we need to use two of them to finish the calculation something plus something is equal to negative five, then the two numbers are negative eight and three.

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