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### Course: Arithmetic (all content) > Unit 4

Lesson 3: Absolute value- Absolute value examples
- Intro to absolute value
- Finding absolute values
- Identify and order absolute values
- Comparing absolute values
- Placing absolute values on the number line
- Compare and order absolute values
- Absolute value as distance between numbers
- Absolute value to find distance
- Absolute value word problems
- Absolute value review

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# Intro to absolute value

Learn how to think about absolute value as distance from zero, and practice finding absolute values.

The absolute value of a number is its distance from $0$ .

For example, the absolute value of $4$ is ${4}$ :

This seems kind of obvious. Of course the distance from $0$ to $4$ is ${4}$ . Where absolute value gets interesting is with negative numbers.

For example, the absolute value of $-4$ is also ${4}$ :

## Let's practice!

## The absolute value symbol

The symbol for absolute value is a bar $|$ on each side of the number.

For example, instead of writing

"the absolute value of $-6$ "

we can just write

## Let's practice!

## Want to join the conversation?

- wouldn't the question -(-7+4)it is absolute, be-11?(38 votes)
- Not quite -

Here's the expression: -|-7 + 4|*First, start by working out the expression***inside***the absolute value bars:*

-|-7 + 4|

-|-3|*Then, take the absolute value of the number inside the bars:*

-|-3|

-(3)

-3*So your answer is -3*

-|-7 + 4| = -3

Hope this helps!(99 votes)

- What is absolute value in real-life scenarios?(14 votes)
- Absolute values are used when we work with distances. Distances are positive values.

For example: A diver is -15 deep (this places him 15 feet below the surface of the water). How far does he need to travel to get to the surface? He needs to travel |-15| = 15 feet.

Hope this helps.(66 votes)

- how is a<|a| shouldn't a=|a| as they are the same distance from 0?(13 votes)
- a was a negative number while absolute a was a positive number therefore a is less than positive a(17 votes)

- Why cant there be negatives for absolute value?(10 votes)
- There are no negatives for absolute value since absolute value is a measure of distance on a number line. (Distance doesn't have negative values only positive

Hopes this helps!(26 votes)

- How last question is solved is explained below:

In place of "a" let's assume number "3", as "a" is placed towards left of "0" it's considered as "-3" (if "a" was placed towards right of "0" we would consider as "+3").

Therefore ==> a = -3

Note Points:

->Negative numbers are always lesser than 0 and positive numbers.

->Positive numbers are always greater than 0 and negative numbers.

-> Absolute of Negative number or Positive number or "0" always results in Positive number.

Now as per the questions asked, lets implement value of "a" that is "-3" and check True or False

Q1.) a < 0 ===> -3 < 0 ===> True

Q2.) |a| > 0 ===> |-3| > 0 ===> 3 > 0 ===> True

Q3.) a < |a| ===> -3 < |-3| ===> -3 < 3 ===> True(20 votes) - this doesn't totally make sense to me.(13 votes)
- So absolute value is the distance a number has from 0. It can never be negative. So lets say that an editor needs to go back -3 pages. The absolute value would be 3. He/she would need to go back 3 pages since there are no negative pages. Hope this helps!(14 votes)

- Can fractions have an absolute value?(11 votes)
- Yes! Think about it is 3/4 of a cm a measurement?

Yes! So, fractions can also have an absolute value.

Hope this helps!(14 votes)

- So this i basicly a washing machine whatever you put in it it becomes celan like lets say 3 is clean and u put it in to the

washing machine (Absloute) and i becomes 3 clean.But if u put -3 whic is dirty it becomes clean when you put it in the machine (Absloute)(17 votes) - If they ask for the absoulte value of 8, is the answer going to be positive 8?(9 votes)
- Yes, because an absolute value can never be a negative number, it can only be positive.(6 votes)

- Would -(-9+3) it be absolute -12(11 votes)
- No. See Jade's question from 2 years ago as it's similar to your question; and Polina's reply/explanation to help you.(9 votes)