Absolute Value of Numbers

It is easiest to think of absolute value as the distance a number is from $$0. Absolute value is represented mathematically by two vertical lines on either side of a value. For example $$|3| means "the absolute value of $$3," $$|−9| means "the absolute value of $$−9" and $$|−x| means "the absolute value of $$−x." 

Let's see the absolute value in action by looking  at a number line. Say we started at $$0 and moved to the number $$3. How many jumps would we make? Three.

Now, let's say we were back at $$0 and moved to the number $$−3. How many jumps would we make? We still have to make three jumps.

Do you see how $$3 and $$−3 are both $$3 units away from $$0? In other words, $$|3|=3 and $$|−3|=3. 

Except for $$0, the absolute value of any real number is the positive value of that number because absolute value is telling us a number's distance from $$0 and we can't have a negative distance. Think about it- we can't walk $$−200 metres! Distances are always positive.

 

Examples

Question 1

What is the value of $$|−155|?

 

Question 2

Add $$|49| and $$|−6|.

 

Question 3

Evaluate each of these numbers, and order the results from smallest to largest:

$$|21|, $$|−7|, $$|−49|, $$|40|

 

Question 4

$$|−20| is greater than which of the following?

A) $$−15    B) $$|−30|     C) $$|−5|     D) $$21

Think: We need to evaluate each of these terms, then answer the answer.

Do:

Let's start by evaluating all the absolute values:

$$|−20|=20, $$|−30|=30 and $$|−5|=5

Which of the four possible answers are smaller than $$20?

So $$|−20| is greater than A) $$−15 and C) $$|−5|