Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 3: Order of Operations and Integers 39

DEFINITION

The number line is a line divided into segments of equal length, labeled with the

integers. Positive numbers increase to the right of zero, and negative numbers go

down to the left.

Absolute Value

The integers came into being because people wanted a way to express opposite ideas like owing

and having, or winning and losing. The number line lets you do that by assigning directions.

Positive numbers go to the right (or up, on a vertical line), and negatives go left (or down).

But sometimes you don’t really care about the direction. You just want to know “how far?” The

absolute value of a number is how far from 0 the number is, regardless of direction. The positive

number 4 is 4 steps away from 0. The absolute value of 4 is 4. The negative number -4 is also 4

steps away from 0, but in the other direction. Absolute value doesn’t care about direction, so the

absolute value of -4 is also 4.

DEFINITION

The absolute value of a number is its distance from zero, without regard to direction.

Absolute value cannot be negative.

The symbol for the absolute value of a number is a set of vertical bars that surround the number.

The absolute value of -9 is written |-9|, so you can write |-9| = 9. If you write |12| = 12, you’re

saying that the absolute value of 12 is 12, or that the number 12 is 12 steps away from 0. The

absolute value symbols can act like parentheses, so if you see arithmetic inside them, do the

arithmetic first, then find the absolute value of the answer.

Find each absolute value.

11. |-19| =


12. |42| =


13. |0| =

14. |5 – 3| =

15. 7 + |5 – 3| =