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## Arithmetic

### Course: Arithmetic > Unit 18

Lesson 2: Negative symbol as opposite# Negative symbol as opposite

Opposites in math involve flipping the sign of a number. A positive number's opposite is the same number but negative, and vice versa. The negative symbol represents the concept of "opposite." When multiple negative symbols are applied, each one flips the number across the number line, resulting in a positive or negative value.

## Want to join the conversation?

- how about in multiplication when -4 x 4 = ?

how about in subtraction?

addition, i already know :D(36 votes)**I know this is 4 years after, but still**.

Think about a number line. When you multiply negative numbers you go more to the left of the number line, where there are more negative numbers. Just like 4x4=16, -4x4=-16. If you multiply +4 by 4, then you're moving to the right of the number line. The same idea applies.(38 votes)

- At0:22, Sal says that he will use this symbol # to represent "number". Where does this symbol come from and why does it represent "number"?(16 votes)
- This has existed for hundreds of years... See the origins section at this link: https://en.wikipedia.org/wiki/Number_sign(20 votes)

- bruh he says opposite so many times in the video(14 votes)
- If you guys don't want to watch the whole video at regular speed just turn it to 2x speed.(14 votes)
- I dont get numbers like-(-7)(3 votes)
- One way to think of a negative sign is just 'inverting' or flipping whatever comes after it. If there is no negative sign, the positive sign (+) is implicit (assumed).

This means that 1 negative sign flips the sign from + to -.

A second negative sign (like -(-7)) flips the first negative sign back to a +.

A third (like -(-(-7))) would flip the sign to - again.

So, an odd number of - signs (1, 3 etc.) gives you a negative number, while an even number of - signs (0, 2 etc) gives you a positive number.(18 votes)

- Math if my worst enemy sadly(10 votes)
- Who argrees that Khan Academy is better than IXL?(7 votes)
- It's probably better, but not by much.(1 vote)

- guys every body like or comment so we can get davinds face reveal(7 votes)
- my name is true(5 votes)
- at3:50he explains that -|-3| when done is positive 3 but shouldn't it be -3(5 votes)
- You are using the absolute value bars which you give the correct answer, but Sal is not talking about absolute value, he uses parentheses such as -(-3) which is two negatives in a row and the answer is positive.(3 votes)

## Video transcript

- [Voiceover] In another video
we've already talked about what an opposite of a number is, but we'll review it a little bit. If we start with a positive number, say, the number four. If you have a number and then we want to think about what the opposite of that number is. Opposite. This is just the symbol for number or shorthand for number. So if the number is four, what is its opposite? Well, four is one, two, three, four to the right of zero. Positive four is four
to the right of zero. So its opposite is going to be one, two, three, four to the left. So it's going to be negative four. Or another way to think about it, if you have a positive number, its opposite is going to be
the negative of that number. So another way of thinking about it is, is that this negative
literally means opposite. One way to think about
it, this is the number that is the opposite of four. So let me write this down. So if I write negative four. Negative, let me write this, negative four. That literally means... So you can take this negative symbol as meaning opposite. Opposite. Opposite of four. Opposite of four. If you were to say negative, instead of saying a specific number let's just say a letter that
could represent a number. So if I said negative A, that means the opposite of the number A. That means the opposite... Opposite of... Let me do that in blue color. Opposite of A. Of A. And if this confuses you
a little bit just look, A could be any number right over here. So let me draw a number line just so this can be a little bit, make a little bit more sense hopefully. So this is a number line. Let me put some tick marks here. I don't know much each
of these tick marks jump but let's say that A is some
number that is right over here. Well negative A is going
to be the opposite of A. So if A is three tick marks to the right negative A is going to be
three tick marks to the left. One, two, three. And so the opposite of A is going to be this value right over here. And we can write that, we can
write opposite of A over here. We could literally write opposite, opposite of A is that number right over there. Or as a shorthand, we can just write-- We can just write negative. We can just write this is
negative A right over here. Negative A. So with that in mind, if we literally view this negative symbol as meaning the opposite
of whatever this is, let's try something interesting. What would be the negative-- Let me do this in another color. What would be the negative of negative three? And I encourage you to pause
the video and think about it. Well we just said, this
negative means the opposite. So you can think about this as meaning this means the opposite... Opposite of negative-- The opposite of negative three. So what is the opposite of negative three? Well negative three is
three to the left of zero. One, two, three. So it's opposite is going to
be three to the right of zero. One, two, three. So it's going to be positive three. So this is equal to positive three. Or we could just write positive three like that. So hopefully this gives
you a better appreciation for what opposite means and also how it relates to the actual negative symbol. We could keep going. We could do something like what is the negative of the negative of negative-- Let me do a different
number. Of negative two. Well, this part right over here the negative, the
opposite of negative two, which is really the opposite
of the opposite of two, well that's just going to be two. Every time you say opposite
you flip over the number line. So this flips you over the
number line two to the left and this flips you back two to the right so all of this is going to be two but then you're going to
take the opposite of two so that's just going to be negative two. If you threw another
negative in front of this, it would be the opposite of all of this. So it would be the
opposite of negative two and then all of a sudden
it would become positive. So every time you put that
negative in front there you're flipping on the other
side of the number line.