# Absolute Value

### Calculating Absolute Value

This page tells you how to calculate absolute value for the ACT math exam.

When you see equations between two vertical lines, you have to find the absolute value.

Remember that absolute values are always positive numbers.

Example 1:

| −17 |  =  17

You might also see questions that involving performing other mathematical operations first.

These types of problems might involve doing addition, subtraction, multiplication, or division or finding a square root of a number.

Example 2:

| −15 + 25 − 50 |  =

| −65 + 25| =

|−40| =

40

You might also see questions that have signs in front of the absolute value symbol. Be especially careful with these types of questions.

Example 3:

− | 21 − 32 |  =

− |  − 9 |  =

− |  9 |  =

− 9

Question 1:

| 15 − 23 |  = ?

A. −12

B. 12

C. −8

D. 8

E. 38

This problem covers the concept of absolute value.

For this problem, you should do the subtraction first:

15 − 23 =  − 8

Now find the absolute value :

| − 8 | = 8

Question 2:

As stated above, you might also see absolute value questions that involve other concepts, such as radicals.

| √4 − 12 |= ?

A. −8

B. −10

C. 8

D. 10

E. 12

For this problem, you should solve the radical first:

√4 = 2

Now substitute 2 in the equation in the place of √4 :

| √4 − 12 | =

| 2 − 12 | =

| −10 | = 10

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