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### 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

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# Number opposites

Learn what it means for a number to be the opposite of another number.

The opposite of a number is the number on the other side of $0$ number line, and the same distance from $0$ .

Here are a couple of examples:

## Let's practice!

## Challenge problems

**Use the following number line for the questions below.**

## Want to join the conversation?

- For opposite numbers I understand how A = -A;

How can A also be E?(133 votes)- A is a variable in this case, so is E. essentially, since they are the same distance from 0, and represent the same amount on the number line, E is just the hidden -A.(127 votes)

- I'm stuck on challenge problem 2A. I would assume that if you have a 0 as the only number on the line, then anything to the left of 0 is a negative number and anything to the right of 0 is a positive. So the opposite number in the same location of A (which is a -A) reflected on the number line is the positive number E. I understand that ideally these would be represented by the same letter, just negative and positives, but I'm working with what is given and expected that the important part is the marks on the number line - not the representative letters used. Help please.(43 votes)
- A is to the left of the 0 on the number line and it's represented simply as an A without a negative. One would assume this is a negative number as the A is just a label for the negative number that's supposedly on that point on the number line.

Taking what we have previously learned, A is a negative number in this case which would mean the opposite of it would be the E on the number line. How could an opposite of a negative number be negative? Unless the number line is flipped in this case?

This left me very confused as the question certainly leads to E being the correct answer.(45 votes)

- I cannot find even a forced logic explanation for problem 2B which I could only guess at given where the 0 is on the number line. Same with 2C. Since the correct answer for problem 2A is: the opposite of A = -A, how did we arrive at A = -E and E = -A?

Mentioned below, previously given only positive letters to work with, how did a negative letter become an answer?

Using a process of elimination to arrive at a "true" answer, does not explain what is happening.

I hope someone will please shed light on how this occurs. So far, I have not found help anywhere.(33 votes)- Hi Catherine C. "Where the 0 is on the number line" is indeed the key clue -- good work noticing it! We arrive at A = -E because A and E are the same distance from 0, but in different directions. One of them is on the negative side of 0, and the other is on the positive side of 0; but they're the same distance.

So, A is the opposite of E. Which means that A is equal to -E. If it's still confusing, try watching the video again.

https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-number-opposites/v/opposite-of-a-number

If it's still confusing after that, post a reply here and, when I get the notification, I'll try to explain better.

As for negative letters -- Well, the letters are variables, standing in for a number. Since numbers can be negative, so can variables.(33 votes)

- I don't understand how A=-E and -A=E?(30 votes)
- This question needs to be revised. It says to use the number line for the questions below (under challenge problems). Problem 2a...Which of the following is the opposite of A? "A" is 3 spaces on the left side of 0 on the number line indicating a negative number. The logical answer would be found 3 spaces to the right of 0, except instead there is E. So the correct selection should be E, yet it is indicated as an incorrect answer ...there is no -A in the location that E occupies (-A was indicated as the correct selection). If the alphabetic characters are indicative of numerical values this should be corrected as it is very confusing to 6th graders. It appears that -A=E ?(28 votes)
- oh yeah , it actually makes sense . A is on the left of 0 but it is not indicated by -A but just A. it is 3 steps to left so its opposite should also be 3 to the lef and it is but represented by E and not A . This is actually really confusing . Wow , I am impressed by this observation Douglas Nelson . :o(10 votes)

- If |-10| shows up it means it is it is positive 10 because if that shows up it can never be negative.(28 votes)
- So those two lines means absolute value which is the numbers distance from Zero therefore it does not matter if the number is a positive or negative it'll always be The same number. Example: |-20| would be 20, Because the distance from -20 from 0 is 20(7 votes)

- why is this sometimes hard(26 votes)
- scroll down to find out

because it tricks you're**brain**(4 votes)

- Why doe negative move to opposite side of 0 on number line?(17 votes)
- Well there is already numbers on the right of the numberline so negative numbers moving to the left of the numberline would make the most sense. There is cases like -3 - (-5) when see the supposed -5 you would think it would be -8 but the answer is 2 in the end, where else would YOU want the negative numberline to be? I think to the left is fine for me.(11 votes)

- yall can someone explain the A= -E thing i seriously dont get it💀(16 votes)
- It may be easier if you give values to the letters, A=-3, B=-1, D=1, and E=3. Thus, there are two pairs of opposites (in math language, they are additive inverses), A and E is one, B and D is the other. One thing that you will learn if you have not already is that additive inverses must add to be 0. Thus, A+E=0. By subtracting one or the other on both sides, you end up with A=-E or E=-A. The same could be true of B=-D or D=-B. Do not know if this is satisfactory to you or not.(12 votes)

- hi can i have upvotes(19 votes)
- It against the rules to ask for upvotes.

If you are trying to get the badge you get when you get 10+ votes, you need to answer someone's question and if people like it, they will vote up your answer. That is how you get the badge. As you can see, you have 20+ votes, and yet no badge.(3 votes)