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### Course: Arithmetic > Unit 18

Lesson 4: Absolute value# Absolute value examples

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.

## Want to join the conversation?

- Wait-- so the absolute value is ALWAYS going to be positive?(462 votes)
- 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)(429 votes)

- What would be the practical application of using an absolute value?(61 votes)
- 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(88 votes)

- is the absolute value aways going to be positive(26 votes)
- 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.(55 votes)

- what is x for is it zero? and why it's cold x?(16 votes)
- X is just a variable, a letter or symbol used to represent an unknown number.(32 votes)

- Is absolute value positive or negative ?(17 votes)
- It is always going to be the positive version of the number(14 votes)

- Do you have to use a number line ?(14 votes)
- No! Number lines are a way to visualize number and also to make things easier(11 votes)

- What does integers mean?(11 votes)
- An integer is a whole number, positive or negative.(20 votes)

- why does absolute value always have to be positive??(11 votes)
- 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.(20 votes)

- Why is the absolute value always positive?(11 votes)
- 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.(16 votes)

- explain what the absolute value of an integer is ?(6 votes)
- The absolute value of an integer is the distance it has from 0 on the number line. And distance is a scalar quantity so it indicates no direction.(5 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.