# Question Video: Arranging Some Given Integers in Ascending Order

Which of the following represents the scores of a board game arranged in ascending order? [A] +9, +3, +6, −1, −3 [B] +9, +6, +3, −3, −1 [C] −3, −1, +3, +6, +9 [D] −3, −1, +6, +3, +9 [E] +9, +6, +3, −1, −3.

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### Video Transcript

Which of the following represents the scores of a board game arranged in ascending order? Well, first let’s think about what ascending order means.

Let’s imagine we’ve got a set of stairs. Now we can either be at the bottom looking up, or we could be at the top looking down.

Now if we were at the bottom looking up and we wanted to go up the stairs, we would call that ascending the stairs, going from the lowest stair to the highest stair. But if we were at the top and wanted to go down, we’d call that descending, going from the highest stair to the lowest stair.

So think of it as descending is going down; we’re going from the highest to the lowest, which means that ascending must be going up in the other direction, going from the lowest to the highest. So ascending means we start at the lowest number and we go up to the highest number.

So let’s just make a note of which way round we’re going: lowest to highest. We’re going up in order. Now let’s think about all those numbers on the number line. All five groupings of numbers include positive nine, positive three, positive six negative one, and negative three. So let’s just mark those on the number line.

Now on a number line, numbers to the left are considered to be smaller than numbers to the right. So in moving from left to right, we’re going up in size or ascending order.

Let’s look at each list of numbers in turn then and think about whether they’re in ascending order or not. So A, it starts off at positive nine and then the next number is positive three. Well we’ve gone from right to left here; we’ve gone from larger to smaller. That’s descending, so that’s not ascending order.

And for B, it starts off with positive nine; the next number is positive six. Again from the first number to the second number, we’ve gone down in size; we’re going from right to left, from larger to smaller. So that’s not ascending order; that’s descending.

Now C, we start off at negative three; we then go to negative one. Well, we’ve gone right there, so we’re still ascending. We then go to positive three. Ooh we’ve gone right again, so that’s ascending. We then go to positive six, and that’s to the right, and then we go to positive nine, and that’s to the right.

So in moving through that list from number to a number, we always got bigger. So we always went from a smaller number to a larger number and moved right on the number line, so the fact that happened in all cases means that that entire list is in ascending order.

Okay, let’s just check out the other two and see if they’re in ascending order as well. So for D, we start off at negative three. We then move to negative one. So that was ascending order; we moved from smaller to larger. We then go to positive six. Well again, we’ve gone from smaller to larger, so that’s still in ascending order. Next we go to positive three. Now for positive three from positive six we’ve gone left, so we’ve now done descending. This is a mixture of ascending and descending order, so that’s not strictly in ascending order.

That’s a bit like A; we went down and then, but then we went up again. So that’s a mixture of descending and ascending order.

And finally let’s consider E. We start off with a positive nine. We then move to positive six. Well that’s to the left; it’s descending. Now let’s just carry on with this one just as an example. We then move to positive three, so that’s descending again. We then move to negative one, so that’s to the left and that’s descending again. And then we go to negative three, and that’s to the left, and that’s descending again. So this E is strictly descending order, which is not what we’re looking for either. So we’ll cross that one off. So our answer is C.

C: negative three, negative one, positive three, positive six, positive nine is in ascending order because each consecutive number moves right on the number line.