Main content

### Course: Algebra basics > Unit 1

Lesson 1: Negative numbers- Intro to negative numbers
- Negative numbers on the number line
- Number opposites
- Number opposites
- Adding numbers with different signs
- Adding negative numbers
- Adding & subtracting negative numbers
- Subtracting a negative = adding a positive
- Subtracting negative numbers
- Multiplying positive & negative numbers
- Why a negative times a negative is a positive
- Why a negative times a negative makes sense
- Dividing positive and negative numbers
- Multiplying negative numbers
- Dividing negative numbers

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Number opposites

Opposites of numbers are essential in understanding number lines and basic math concepts. The opposite of a positive number is its negative counterpart, while the opposite of a negative number is its positive counterpart. Both numbers have the same absolute value but different signs, making them equally distant from zero on the number line.

## Want to join the conversation?

- How do you find a opposite from a fraction?(43 votes)
- There are negative fractions; these are the opposites of positive fractions. If you had 3/4 for instance, it's opposite is -3/4. There is also something else you can sorta classify as a opposite of a fraction-- its
*reciprocal*. A reciprocal is just the fraction turned upside down; the reciprocal of 3/4 is 4/3. Hope I helped :)(60 votes)

- So basically whatever the positive number is, the opposite would be the same digit but with a negative at the front?(29 votes)
- Yes a positive number with a negative in front of it.(18 votes)

- How do you find the opposite of a fraction?(12 votes)
- To find the opposite of a fraction you just do the same thing you would do with a whole number. If you need to find the opposite of -4 1/2 , you can find the opposite of -4, Which is 4, then add the 1/2.(12 votes)

- negative numbers are useful in real life,but why do we need to learn opposites?(10 votes)
- to make us understand negatives(14 votes)

- what is the opposite of -20(7 votes)
- 20 because it's the same distance from zero as -20(19 votes)

- if the opposite of a number is the number the same distance from 0 what is the opposite.(10 votes)
- It is the same number, just it is a
**negative**instead. If it is already a**negative**, than it is the same number but a**positive**instead.(10 votes)

- I heard about the function
`absolute value`

and I did not understand what it meant.

could anybody explain please?(9 votes)- The number's value from zero. For example, if you are standing on a starting line and walk backwards 7 meters you could say you went -7 meters distance (in other words you would have to go 7 meters just to get back to zero, or the starting line). However, the absolute value of how far you have walked would be 7 meters, not -7. In essence, it removes the negative from negative numbers, giving only their value (so -7 becomes 7, -215 becomes 215, etc.)(12 votes)

- Here's a hard one:

-3+-(4)(8 votes)- If the signs are the same, you add and keep the sign, and if they are different you subtract and keep the sign of the larger number. So -3+-4 is -7(10 votes)

- how do you subtract negative numbers(6 votes)
- Add them together and then make them negative I believe(14 votes)

- what's the opposite of 0? it's just 0 lol. Is zero positive or negative? PLease answer, buddies!(6 votes)
- Zero doesn't fall under either category. It's similar to how 1 isn't considered a composite or prime number. It's a unique case! Thank you for asking! ❤❤❤(8 votes)

## Video transcript

- [Voiceover] What I want
to do in this video is think about what it means to
have an opposite of a number. Let me draw a number line here. Let's draw a number line. And let's put some numbers
on this number line. We can start at zero, and if we go to the right
we have positive numbers. One, two, three, four, five. As we go to the left we
get more and more negative. So negative one, negative
two, negative three, negative four, and I can
keep going on and on and on. Let's pick one of these numbers. Let's say that we pick the number three. What is going to be the
opposite of the number three? Well the opposite of the
number is a number that's the same distance from
zero but on the other side. So three is three to the right of zero. One, two, three. So its opposite is going to
be three to the left of zero. One, two, three. So the opposite of
three is negative three. Let me make a little table here. If we have the number, the number. And then we have its opposite. We have its opposite. So we just figured out that
if you have the number three, its opposite is going
to be negative three. Now what if your number is negative? What if your number, let's
say the number negative four. What's the opposite of that? And I encourage you to pause the video and try to think about it on your own. Well, you say, okay, negative
four is right over here. That's negative four. It is four to the left of zero. One, two, three, four to the left of zero. So its opposite is going to
be four to the right of it. So one, two, three, four. It's going to be positive. It's going to be positive four. So you're probably starting
to see a pattern here. The opposite of a number is going to be the opposite sign of that number. If you have a positive three here, its opposite is going
to be negative three. If you start with negative four, its opposite is going to be positive four. One way to think about
it, it's going to have the same absolute value but
have a different sign. Or another way to think about it is, however if this is three
to the right of zero, its opposite is going to be
three to the left of zero. Or if the number is four
to the left of zero, its opposite is going to be
four to the right of zero. So we'll do one last one. What is the opposite of... What's going to be the opposite of one? Well one is one to the right of zero, so its opposite is going to
be one to the left of zero, or negative one. Or another way to think
about it, one is positive so its opposite is where you're
going to change the sign. Instead of being positive
it's going to be negative. It's going to be negative one. Either way that you can think about it.