Absolute value
Absolute Value and Number Lines Absolute Value and Number Lines
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- We're told to plot these values on a number line.
- And you see every one of these values
- have an absolute value sign.
- So let's take a little bit of a review of
- what absolute value even is.
- Absolute value
- The way I think about it,
- there's two ways to think about it.
- The first way to think about it is,
- how far is something from 0?
- So let me plot this negative 3 here.
- So let me do a number line.
- This isn't the number line for our actual answer,
- or to this command, plot these values on a number line.
- I'm just first going to plot the numbers
- inside the absolute value sign,
- and then we're going to take the absolute value
- and plot those,
- just like they're asking us to do.
- So on this number line, if this is 0,
- if we go to the negative
- we're going to go to the left of 0.
- So this is negative 1, negative2, negative 3.
- Negative 3 sits right over there,
- so this is negative 3 right there.
- The absolute value of negative 3 is essentially saying
- how far are you away from 0?
- How far is negative 3 from 0?
- And you say, well, it's 1, 2, 3 away from 0.
- So you'd say that the absolute value of negative 3 is
- equal to positive 3.
- Now that's really the conceptual way to imagine absolute value.
- How far are you away from 0?
- But the easy way to calculate absolute value signs,
- if you don't care too much about the concept is
- whether it's negative or positive,
- the absolute value of it is
- always going to be positive.
- Absolute value of negative 3 is positive 3.
- Absolute value of positive 3 is still positive 3.
- So you're always going to get
- the positive version of the number, so to speak.
- But conceptually,
- you're just saying how far away are you from 0.
- So let's do what they asked.
- So that first value, on this number line,
- so all of these are absolute values.
- So they're all going to be positive values.
- So they're all going to be greater than 0.
- So let me draw my number line like this.
- I can do a straighter number line than that.
- Let's see. Well, that's a little bit straighter.
- And let's say, if this is 0,
- this would be negative 1,
- then you'd have 1, 2, 3, 4, 5, 6, 7.
- I think that'll do the trick.
- So this first quantity here,
- I'll do it in orange,
- the absolute value of negative 3,
- we just figured out, that is positive 3.
- So I'll plot it right over there, positive 3.
- Then this next value,
- right here, the absolute value of 7.
- If we look over here,
- 1, 2, 3, 4, 5, 6, 7.
- 7 is how far away from 0?
- It is 7 away from 0.
- So the absolute value of 7 is equal to 7.
- So you already see the pattern there.
- If it's negative, it just becomes positive.
- If it's already positive, it just equals itself.
- So plotting this value,
- I'll just place it right over there.
- So the absolute value of 7 is 7.
- Absolute value of negative 3 is positive 3.
- Let me mark out the 0 a little bit better,
- so you see relative to 0.
- Now we have the absolute value of 8 minus 12.
- Well, first of all,
- let's figure out what 8 minus 12 is.
- So if you take 12 away from 8,
- you're at negative 4.
- 12 less than 8 is negative 4.
- And you can do that on a number line,
- if you don't quite remember how to do this.
- But if you, you know
- if you take 8 away from 8,
- you're at 0, and then you take another one,
- you're at negative 1,
- then negative 2, negative 3, all the way to negative 4.
- So this is equal to the absolute value of negative 4.
- If we just plot negative 4, we go 1, 2, 3,
- negative 4 is right over there.
- But if we're taking its absolute value,
- we're saying, how far is negative 4 from 0?
- Well it's 4 away from 0.
- 1, 2, 3, 4. So this is equal to positive 4.
- So we'll plot it right here.
- This number line is
- the answer to this command up here.
- So the absolute value of 8 minus 12,
- which is negative 4, is positive 4.
- Then we have the absolute value of 0.
- So how far is 0 from 0?
- Well, it's 0 away from 0.
- The absolute value of 0 is 0,
- so you can just plot it right over there.
- And we have one left.
- Let me pick a suitable color here.
- The absolute value of 7 minus 2.
- Well, 7 minus 2 is 5,
- so this is the same thing as
- the absolute value of 5.
- How far is 5 away from 0?
- Well, it's just 5 away.
- It's almost, you know, too easy.
- That's what makes it confusing.
- If I were to plot 5, it's 1, 2, 3, 4, 5.
- It is 1, 2, 3, 4, 5 spaces from 0.
- So the absolute value of 5 is 5.
- So you plot it just like that.
- So conceptually,
- it's how far you are away from 0.
- But if you think about it
- in kind of just very simple terms,
- if it's a negative number,
- it becomes a positive version of it.
- If it's a positive number already,
- it just equals itself,
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