If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

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:
4 is the opposite of 4.
3 is the opposite of 3.

Let's practice!

Problem 1A
Move the dot to the opposite of 2.

Challenge problems

Use the following number line for the questions below.
Problem 2A
Which of the following is the opposite of A?
Choose 1 answer:

Want to join the conversation?

  • blobby green style avatar for user figueroa
    For opposite numbers I understand how A = -A;
    How can A also be E?
    (136 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user maria
    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)
    Default Khan Academy avatar avatar for user
    • starky seedling style avatar for user Hamad
      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.
      (46 votes)
  • duskpin ultimate style avatar for user Catherine C
    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)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user shaikha.radgollcat
    I don't understand how A=-E and -A=E?
    (31 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Douglas Nelson
    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)
    Default Khan Academy avatar avatar for user
    • duskpin sapling style avatar for user NASA _Girl
      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)
  • male robot hal style avatar for user sean.li
    If |-10| shows up it means it is it is positive 10 because if that shows up it can never be negative.
    (28 votes)
    Default Khan Academy avatar avatar for user
  • female robot amelia style avatar for user DEXTER WASHINGTON
    why is this sometimes hard
    (26 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user David McCauley
    Why doe negative move to opposite side of 0 on number line?
    (17 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user 2606126
      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)
  • blobby green style avatar for user maddy bauer
    yall can someone explain the A= -E thing i seriously dont get it💀
    (16 votes)
    Default Khan Academy avatar avatar for user
    • mr pink green style avatar for user David Severin
      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.
      (13 votes)
  • blobby green style avatar for user khronograf
    hi can i have upvotes
    (20 votes)
    Default Khan Academy avatar avatar for user