Calculating Absolute Value – Exercises
Instructions: Try the absolute value exercises below. The answers and explanations are provided in the next section. You may want to look at the examples in the last section of this page before you do the exercises.
1. | −83 | = ?
2. | −16 + 14 − 28 | = ?
3. −| −42 | = ?
4. −| 21 − 32 | = ?
5. −|−25 – 45 − 15 | = ?
6. −|−14 + 8 + 36 | = ?
7. |√16 − 6 | = ?
8. −|x2 + 5 | = ?
9. −|x2 + y2 | = ?
10. −|√4 − 49 | = ?
Answers to the Exercise
1. | −83 | = 83
2. | −16 + 14 − 28 | = | −2 − 28 | = |−30| = 30
3. −| −42 | = −| 42 | = −42
4. −| 21 − 32 | = −|−11 | = −| 11 | = −11
5. −|−25 – 45 − 15 | = −|−70 − 15 | = −|−85 | = −85
6. −|−14 + 8 + 36 | = −|−6 + 36 | = -30
7. |√16 − 6 |= | 4 – 6| = |-2| = 2
8. −|x2 + 5 | = −(x2 + 5)
9. −|x2 + y2 | = −(x2 + y2)
10. −|√4 − 49 |= -|2 – 49| = -47
Absolute Value Examples
Absolute value is represented as a number, variable, or equation between the absolute value signs: | |
Example 1:
Remember that absolute values are always positive numbers.
| −25 | = 25
Example 2:
You might see questions that involving performing other mathematical operations first.
These types of problems might involve addition, subtraction, multiplication, or division.
| −15 + 25 − 50 | =
| −65 + 25| =
|−40| =
40
Example 3:
You might also see questions that involve other concepts, such as radicals or squared numbers inside the absolute value signs.
For the problem below, you should solve the radical first by substituting 2 in the equation in the place of √4 :
| √4 − 12 |=
| 2 − 12 | =
| −10 | = 10
Example 4:
When you see a negative sign outside of the absolute values, you need to make your final answer negative.
That is because the negative of an absolute value is always negative.
− | 21 − 32 | =
− | − 9 | =
− | 9 | =
− 9
More ACT Practice
Try our free sample test.
Then check your answers.
