Wait-- so the absolute value is ALWAYS going to be positive?

Apart from zero, yes always positive, it's a measure of distance from 0 on the number line (either to the left or the right)

What would be the practical application of using an absolute value?

http://mathforum.org/library/drmath/view/57177.html -1. Distances in real life: suppose you go three blocks east, then six blocks west, then eleven blocks east again. Now we can ask two questions: Where are you relative to where you started? This requires us to retain the sign information, and is not answered by the absolute value. The other obvious question is "How far did you go?" Now every student in your class should add 3 + 6 + 11, each of them doing at least one

is the absolute value aways going to be positive

Good question. The answer is...yes...and no! The precise term in "non-negative." Absolute value is a magnitude and is either positive or zero. Zero is neither positive nor negative. But the absolute value of any non-zero number can be thought of as it's distance from zero and it will always be positive.

Is absolute value positive or negative ?

It is always going to be the positive version of the number

what is x for is it zero? and why it's cold x?

X is just a variable, a letter or symbol used to represent an unknown number.

why does absolute value always have to be positive??

The absolute value is the distance. Imagine being in a car. Even if the car drives backwards all the way to the destination (which is possible), there will still be distance traveled. Just because it is backwards doesn't mean that it goes negative distance. Same for negative numbers. If there is an absolute value of a negative number (l-6l), the distance of it away from zero cannot be a negative distance. So if the distance is always positive, then the absolute value will always be positive.

Do you have to use a number line ?

No! Number lines are a way to visualize number and also to make things easier

What does integers mean?

An integer is a whole number, positive or negative.

Why is the absolute value always positive?

The absolute value of a number means the distance from 0. -5 is 5 units away from 0. So the absolute value of that -5 is 5. You cannot have negative distance, so it has to be positive.

ok this helped a lot ty and basically 5 to the absolute value is 5 but negative 5 to the absolute value is also 5? right?

Yes, absolute value is simply the distance from zero. The absolute value of 5 is the same thing as the distance from zero to 5. Therefore, the absolute value of 5 is 5. You are correct for negative 5 as well. The distance between -5 and 5 from zero is the same, and -5 in absolute value is also 5. Hope this helps!

Main content

6th grade

Course: 6th grade > Unit 5

Lesson 6: Intro to absolute value

Absolute value examples

Name: Absolute value examples
Uploaded: 2011-02-20T16:40:17Z
Description: The absolute value of a number represents its distance from zero on a number line, always resulting in a positive value. This concept is essential in mathematics, as it helps to simplify calculations and understand the magnitude of numbers, regardless of their positive or negative sign. Examples include finding the absolute values of 5, -10, and -12.

Google Classroom

The absolute value of a number represents its distance from zero on a number line, always resulting in a positive value. This concept is essential in mathematics, as it helps to simplify calculations and understand the magnitude of numbers, regardless of their positive or negative sign. Examples include finding the absolute values of 5, -10, and -12. Created by Sal Khan and Monterey Institute for Technology and Education.

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Kittycat12
Posted 11 years ago. Direct link to Kittycat12's post “Wait-- so the absolute va...”
Wait-- so the absolute value is ALWAYS going to be positive?
Button navigates to signup pageComment on Kittycat12's post “Wait-- so the absolute va...”
(448 votes)
Answer
- Paul
  Posted 11 years ago. Direct link to Paul's post “Apart from zero, yes alwa...”
  Apart from zero, yes always positive, it's a measure of distance from 0 on the number line (either to the left or the right)
  Comment on Paul's post “Apart from zero, yes alwa...”
  (408 votes)
Thomas Keegan
Posted 11 years ago. Direct link to Thomas Keegan's post “What would be the practic...”
What would be the practical application of using an absolute value?
Button navigates to signup pageComment on Thomas Keegan's post “What would be the practic...”
(54 votes)
Answer
- sameer
  Posted 11 years ago. Direct link to sameer's post “http://mathforum.org/libr...”
  http://mathforum.org/library/drmath/view/57177.html -1. Distances in real life: suppose you go three blocks east, then six
  blocks west, then eleven blocks east again. Now we can ask two
  questions: Where are you relative to where you started? This
  requires us to retain the sign information, and is not answered by
  the absolute value. The other obvious question is "How far did you
  go?" Now every student in your class should add 3 + 6 + 11, each of
  them doing at least one
  Comment on sameer's post “http://mathforum.org/libr...”
  (77 votes)
Justin Cheng
Posted 7 years ago. Direct link to Justin Cheng's post “is the absolute value awa...”
is the absolute value aways going to be positive
Button navigates to signup pageComment on Justin Cheng's post “is the absolute value awa...”
(23 votes)
Answer
- Paul Miller
  Posted 7 years ago. Direct link to Paul Miller's post “Good question. The answe...”
  Good question. The answer is...yes...and no! The precise term in "non-negative." Absolute value is a magnitude and is either positive or zero. Zero is neither positive nor negative. But the absolute value of any non-zero number can be thought of as it's distance from zero and it will always be positive.
  Comment on Paul Miller's post “Good question. The answe...”
  (47 votes)
Katori Machi
Posted 7 years ago. Direct link to Katori Machi's post “what is x for is it zero?...”
what is x for is it zero? and why it's cold x?
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(11 votes)
Answer
- Ron Dang
  Posted 7 years ago. Direct link to Ron Dang's post “X is just a variable, a l...”
  X is just a variable, a letter or symbol used to represent an unknown number.
  Comment on Ron Dang's post “X is just a variable, a l...”
  (27 votes)
Vishnu Prabhav
Posted 5 years ago. Direct link to Vishnu Prabhav's post “Is absolute value positiv...”
Is absolute value positive or negative ?
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- Dev
  Posted 3 years ago. Direct link to Dev's post “It is always going to be ...”
  It is always going to be the positive version of the number
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  (9 votes)
Destiney salazar
Posted 7 years ago. Direct link to Destiney salazar's post “why does absolute value a...”
why does absolute value always have to be positive??
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Answer
- istegis
  Posted 7 years ago. Direct link to istegis's post “The absolute value is the...”
  The absolute value is the distance. Imagine being in a car. Even if the car drives backwards all the way to the destination (which is possible), there will still be distance traveled. Just because it is backwards doesn't mean that it goes negative distance. Same for negative numbers. If there is an absolute value of a negative number (l-6l), the distance of it away from zero cannot be a negative distance. So if the distance is always positive, then the absolute value will always be positive.
  Comment on istegis's post “The absolute value is the...”
  (15 votes)
Daniyal Khan
Posted 10 years ago. Direct link to Daniyal Khan's post “What does integers mean?”
What does integers mean?
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(9 votes)
Answer
- Cyrus Hatam
  Posted 10 years ago. Direct link to Cyrus Hatam's post “An integer is a whole num...”
  An integer is a whole number, positive or negative.
  Comment on Cyrus Hatam's post “An integer is a whole num...”
  (16 votes)
CRONAVIRUSMMMMMMMMMM 🥵🤢🤮🙉😷
Posted 3 years ago. Direct link to CRONAVIRUSMMMMMMMMMM 🥵🤢🤮🙉😷's post “Do you have to use a numb...”
Do you have to use a number line ?
Button navigates to signup pageComment on CRONAVIRUSMMMMMMMMMM 🥵🤢🤮🙉😷's post “Do you have to use a numb...”
(10 votes)
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- 25vincentmejia
  Posted 2 years ago. Direct link to 25vincentmejia's post “No! Number lines are a wa...”
  No! Number lines are a way to visualize number and also to make things easier
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  (5 votes)
Jonathan M.
Posted 10 years ago. Direct link to Jonathan M.'s post “Why is the absolute value...”
Why is the absolute value always positive?
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(6 votes)
Answer
- Benny C
  Posted 10 years ago. Direct link to Benny C's post “The absolute value of a n...”
  The absolute value of a number means the distance from 0.
  -5 is 5 units away from 0. So the absolute value of that -5 is 5.
  You cannot have negative distance, so it has to be positive.
  Comment on Benny C's post “The absolute value of a n...”
  (13 votes)
hanakbasit
Posted 2 months ago. Direct link to hanakbasit's post “ok this helped a lot ty a...”
ok this helped a lot ty and basically 5 to the absolute value is 5 but negative 5 to the absolute value is also 5? right?
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- 🅹🅾🅷🅽🅽🆈
  Posted 2 months ago. Direct link to 🅹🅾🅷🅽🅽🆈's post “Yes, absolute value is si...”
  Yes, absolute value is simply the distance from zero. The absolute value of 5 is the same thing as the distance from zero to 5. Therefore, the absolute value of 5 is 5. You are correct for negative 5 as well. The distance between -5 and 5 from zero is the same, and -5 in absolute value is also 5.
  
  Hope this helps!
  Comment on 🅹🅾🅷🅽🅽🆈's post “Yes, absolute value is si...”
  (7 votes)

Video transcript

Find the absolute value of x when x is equal to 5, x is equal to negative 10, and x is equal to negative 12. So the absolute value, the way of writing it is almost more complicated than what it really is. The absolute value is really just the distance of x from 0. So let me just draw a fast number line over here. So let's just put 0 right over here, since we're thinking about the distance from 0. So let's just think about the absolute value. Let's think about the absolute value of x when x is equal to 5. So that's equivalent to the absolute value of 5. We just substituted 5 for x. The absolute value of 5 is the distance of 5 from the 0. So you go 1, 2, 3, 4, 5. 5 is exactly 5 to the right of 0. So the absolute value of 5 is just 5. Now I think you already get to see this is a pretty straightforward concept. Now let's do something a little more interesting, the absolute value of x when x is equal to negative 10. So let's just put negative 10 in for x. This is the distance that negative 10 is from 0. And so let's just go negative 1, negative 2, negative 3, negative 4, negative 5, negative 6, negative 7, negative 8, negative 9, negative 10. I should extend the number line more. So this right here is negative 10. So how far is it away from 0? Well, it's 10 to the left of 0. So you put a 10 here. And so in general, absolute value will always be a positive quantity. And when we're rethinking about just absolute values of just numbers, it's just going to be, really, the positive version of that number. Let's do one more. Well, they tell us to do one more, the absolute value of x when x is equal to negative 12. So we have the absolute value of negative 12. We don't even to look at the number line. It's just going to be the positive version of negative 12. It's just going to be equal to 12. And this is just saying that negative 12 is 12 away from 0. And we could draw it over here. This is negative 11. Negative 12 is right over here. It is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 away from 0.