Introduction to Absolute Value:

The absolute value of a number is the number's distance from zero on a number line. 

Since we never talk about distance as being negative, the absolute value of a number is always positive. Think of it as the number of jumps it would take to get to zero from a number. 

Number Line-Distance from 0

  • It would take five jumps to get to zero from -5, so the absolute value of -5 is 5. 
  • It would also take five jumps to get to zero from +5, so the absolute value of +5 is also 5.

We use bars (vertical lines) on either side of a number absolute to mean absolute value.

    |-4| = the absolute value of -4 = 4

Pretty simple. If the number is negative, make it positive. If the number is already positive, leave it alone.

Absolute Value Practice:

Example 1

|-3| + |2|

Treat absolute value bars as parentheses; do what is inside first.  Take the absolute value of (-3) and add to that the absolute value of (+2).


Example 2

-|-6|

Treat absolute value bars as parentheses; do what is inside first. Take the absolute value of -6, then take the negative of that number.


Example 3

|7 - 9|

Again, treat absolute value bars as parentheses, do what is inside first, then take the absolute value.


Example 4

|-5 + 3| - |-2 - 1|

Treat each set of absolute value bars as a set of parentheses. Simplify each separately, then subtract.


Exercise 1

|-16|


Exercise 2

|-30| + |-5|


Exercise 3

-|15 + 2|


Exercise 4

|-4 + 1| + |-10|


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