Pre-Algebra

Absolute Value

Lesson

The absolute value of a number is its distance from zero on the number line. Distance is never negative, so absolute value is always $0$ or positive.

Write absolute value with vertical bars: $|x|$ means the absolute value of $x$ .

The rule

If the number is positive or zero, $|x| = x$ .
If the number is negative, $|x| = -x$ (drop the negative sign).

Worked example 1

|-7| = 7

$-7$ is 7 units from zero.

Worked example 2 — evaluate inside first

|3 - 8|

Compute inside the bars first: $3 - 8 = -5$ . Then take the absolute value: $|-5| = 5$ .

Worked example 3 — distance between two points

On a number line, distance from $a$ to $b$ is $|a - b|$ . Distance from $-3$ to $4$ :

|-3 - 4| = |-7| = 7

Watch out

Always do the arithmetic inside the bars first, then take the absolute value. $-|5|$ is $-5$ — the negative is outside.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

|5|

Problem 2

|-3|

Problem 3

|0|

Problem 4

|-12|

Practice

Standard problems matching the lesson.

Problem 5

|-8|

Problem 6

|17|

Problem 7

|3 - 10|

Problem 8

|2 - 9|

Problem 9

|6| + |-4|

Problem 10

|-5| - |2|

Problem 11

|-3| \times |4|

Problem 12

|-20| \div |5|

Problem 13

-|9|

Problem 14

-|-6|

Problem 15

|-1 - 4|

Problem 16

|7 - 7|

Problem 17

|-85|

Problem 18

|-14|

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

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

Problem 20

|5 - 12| + |-3|

Problem 21

|-4| \times |-2| - |3|

Problem 22

|3 \times -4|

Problem 23

|-6 - 4|

Problem 24

|-8 - 5|

Problem 25

|-15 - (-42)|

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