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## 6th grade (Eureka Math/EngageNY)

### Course: 6th grade (Eureka Math/EngageNY) > Unit 3

Lesson 1: Topic A: Understanding positive and negative numbers on the number line- Introduction to negative numbers
- Intro to negative numbers
- Negative numbers on the number line
- Interpreting negative numbers
- Negative decimals on the number line
- Negative decimals on the number line
- Decimals & fractions on the number line
- Negative fractions on the number line
- Missing numbers on the number line examples
- Missing numbers on the number line
- Number opposites
- Number opposites
- Number opposites
- Negative symbol as opposite
- Negative symbol as opposite
- Number opposites review

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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:

start color #e84d39, minus, 4, end color #e84d39 is the opposite of start color #1fab54, 4, end color #1fab54.

start color #1fab54, 3, end color #1fab54 is the opposite of start color #e84d39, minus, 3, end color #e84d39.

## 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?(74 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.(57 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.(34 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.(28 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.(25 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.(24 votes)

- Why doe negative move to opposite side of 0 on number line?(10 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.(4 votes)

- this is so weird i dont undersand how a= -a(7 votes)
- A=-A because -A is the opposite of A(5 votes)

- Question 2A is extremely confusing. Point "A" is to the left of 0. It's opposite should be the point which is the same distance to the right of 0, which is E. If I understand the lesson correctly point "A" should be negative because it is to the left of 0; and point "E" should be positive, which it is, but there is no corresponding answer. Please explain this.(6 votes)
- They want you to understand that "E" and "negative A" (or, "opposite of A") are the same. If they gave "E" as a possible answer, people might choose that without grasping that -A is the same thing.(6 votes)

- it keeps saying cant grade your answer(6 votes)
- You usually get that message when your answer is in the wrong format; or you have extra characters like spaces that it isn't expecting.

Use the hints - compare your work and answer to that found in the hint. This will likely help you figure out why you are getting that error message.(4 votes)

- Also for the next one HOW! JUST HOW! are those correct You just said that A=E so that is kinda hard on my side aparentley ( A=-E and E=-A ) so this makes me mad with the lack of info this gives me(7 votes)
- for opposite numbers I understand how A = -A;

How can A also be E?(6 votes)- if A=-A then A=0(3 votes)

- how is a=a. i couldin understand it(6 votes)
- a=a because a is on the same side as a(1 vote)