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Lesson 1: Absolute value

# Absolute value as distance between numbers

In this video, we think about what |a-b| really means, and we verify that |a-b| = |b-a| by looking at an example.

## Want to join the conversation?

• why 3-(-2) = 5? Could you please give me a example in real world to explain this equation?
• i don't get it how does -5 equal 5
• Absolute value basically measures how far the number is from zero. If you think about a number line, -5 is the same distance away from 0 as 5 is.
Putting an absolute value on something isn't really saying that they are the same number, but it's saying that they are the same distance away from 0.
• Can you help me further understand this concept? I don't really understand how to work it out.
• Every number that are inside the I I becomes positive.
ex)1. I -6 I = I 6 I
2. I -5-2 I = I -7 I = I 7 I
• The practice & exam problems bringing in fractions and decimals is really throwing me off. I looked through the comments, but I don't see any examples that actually address this nor does Sal give any examples.
• With fractions and decimals solving for absolute value is the same process. If I have l 3/4 l and
l -7/6 l being compared then the absolute value of 7/6 is greater.
• Is there a special name for this phenomenon of a formula |a-b| = |b-a|?
• This phenomenon is called commutativity.
So the property |a-b| = |b-a| means that the distance between two numbers is a commutative operation.
• this is not really a question but how does he draw straight lines perfectly??
• i still don't get how the absolute value of a-b is the same as the absolute value of b-a. Please help.
(1 vote)
• Consider the following:
You have one value, a, that is 3; so a = 3
You also have another, b, that is 7; so b = 7
So a - b = 3 - 7= -4, while b - a = 7 - 3 = 4

When you take the absolute value of either equation (|a - b| or |b - a|), you can see that both result in an answer of 4, as the negative result of a - b (-4) still has a positive absolute value (4).

Let me know if this clarifies, or if you have any further questions!
• Does it always have to be number lines?
Does anyone know of an alternative way to do this?
Also, can anyone properly explain this to me?
Thank You
• No, it does not always have to be on a number line; this is showing you how to do this if you don't have a number line. Since you know you can subtract the number further on the left on the number line from the number on the right to find the distance between, a number line is easy. However, if you have two variables without a number line, you can't know which is greater, so you can't subtract without using this strategy. Since |a-b| = |b-a|, as long as we find the absolute value of the answer, we can subtract in any order.