Absolute Value

The absolute value of a number, denoted by vertical lines surrounding the number, is the positive distance between the number and zero on the number line. It is the value of the corresponding "unsigned" number--either itself or its opposite: the absolute value of a positive number is the positive number, and the absolute value of a negative number is its opposite. More simply put, the absolute value of a number is the number with the sign removed. The absolute value of -3, denoted | - 3|, is 3. The absolute value of 15, denoted | 15|, is 15. The number inside the absolute value sign need not be an integer. For example, | - 5/2| = 5/2.

Computation with Absolute Value

To evaluate an expression that contains an absolute value, first carry out the expression inside the absolute value sign. Next, take the absolute value of the resulting number. Then evaluate the expression according to the order of operations.

Examples:

13 + | 2 - 3| + | 5×6| = 13 + | - 1| + | 30| = 13 + 1 + 30 = 44

34 - | 3×(- 4)| + | 4×2 - (- 5)| = 34 - | - 12| + | 13| = 34 - 12 + 13 = 35

| 56 - (- 8)|/| - 6 - 2|×(- 1/4) = | 64|/| - 8|×(- 1/4) = 64/8×(- 1/4) = - (8×1/4) = - 2