Absolute Value of Numbers

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

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

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

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

Except for $0$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$0 and we can't have a negative distance. Think about it- we can't walk $-200$−200 metres! Distances are always positive.

 

Examples

Question 1

What is the value of $\left|-155\right|$|−155|?

 

Question 2

Add $\left|49\right|$|49| and $\left|-6\right|$|−6|.

 

Question 3

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

$\left|21\right|$|21|, $\left|-7\right|$|−7|, $\left|-49\right|$|−49|, $\left|40\right|$|40|

 

Question 4

$\left|-20\right|$|−20| is greater than which of the following?

A) $-15$−15    B) $\left|-30\right|$|−30|     C) $\left|-5\right|$|−5|     D) $21$21

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

Do:

Let's start by evaluating all the absolute values:

$\left|-20\right|=20$|−20|=20, $\left|-30\right|=30$|−30|=30 and $\left|-5\right|=5$|−5|=5

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

So $\left|-20\right|$|−20| is greater than A) $-15$−15 and C) $\left|-5\right|$|−5|