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## Arithmetic (all content)

### Course: Arithmetic (all content)>Unit 4

Lesson 2: Number opposites

# Number opposites challenge problems

Sal solves a few challenging problems with number opposites on the number line.

## Video transcript

- [Voiceover] So let's do a couple of examples of the number opposites exercise on Khan Academy. Just to make sure that we've really digested what it means to be the opposite of a number. So they have a number line here, and then they've marked some of the numbers with letters. And this is A, B, C, D, E. And then they say, "What can we say about point B?" And point B is one hash mark to the left of zero, all right. "Select all that applies." So the first thing, they say is, "B is equal to negative D." So that means that B needs to be the opposite of D. Let's see if that's true. D is here. D is one hash mark to the right of zero. The opposite of D, or negative D, should be one hash mark to the left of zero. Which is B. B is the opposite of D. B is negative D, so this is true. The next statement is, "B is the opposite of E." Let's see, E is one, two, three hash marks to the right of zero. So the opposite of E should be one, two, three hash marks to the left of zero. That is not B; that is A. B is not the opposite of E. A is the opposite of E, but that isn't what they write here so we're not going to check that. And then they say, "B is equal to negative B." That's saying that B is the same thing as the opposite of B. That is not true. The opposite of B is going to go on the other side of the number line. That's D, which is not B. So this is also not true. This would have been true if they said, "C is equal to negative C." Because C is at zero, it's zero away from zero. C is zero. The opposite of zero is going to be zero away on the other side of the number line. Well, that's still zero away. So zero is negative zero. Or we could have said C is equal to negative C. But the only number for which that is true is zero. It's not going to be true for B, because B is clearly not zero. So let's do a couple of here. "What can we say about negative C?" All right, so now C is zero. "Select all that apply." "Negative C is zero." Yeah, the negative of zero is going to still be zero. The negative of zero, the opposite of zero, is still going to be zero. The opposite of zero, that's not going to be this number. This is some non-zero number. So that's that. All right. "What can we say about point T?" T once again is at zero. So we say, "T is zero." "Zero is the opposite of zero." It is equal to negative zero. Both of them -- one is zero, you could say zero to the left, one is zero to the right. Well, that still means that they're still on zero. And they're right, they are zero. "T is equal to the opposite of the opposite of T." Well, this would actually be true for any number. For any number, the opposite of the opposite is going to be that number. We could have put the Q here, the R here. Really for any number the opposite of the opposite is going to be that number again. And so it's definitely going to be true for zero as well. So that's definitely going to be true. So hopefully that kind of gives you a little bit more practice with number opposites and helps you digest things a little bit more.