Absolute Value Worksheet — Math Practice for 13-Year-Olds (Middle School)

Instructions

Read the explanation of absolute value below. Then, work through the problems in each section. Remember, absolute value is all about distance from zero!

Part 1: What is Absolute Value?

The absolute value of a number is its distance from zero on a number line. Since distance is always a positive value (you can't travel a negative distance!), the absolute value of a number is always positive or zero.

Think of it like taking steps. If you are standing at zero, taking 8 steps forward (+8) and taking 8 steps backward (-8) both result in you being 8 steps away from where you started.

The symbol for absolute value is two vertical bars: | |.

• So, we would write |-8| = 8, which is read as "The absolute value of negative eight is eight."
• We would also write |8| = 8, which is read as "The absolute value of eight is eight."

Part 2: Find the Value

Solve the following absolute value expressions.

1. |-12| =
2. |35| =
3. |0| =
4. |-250| =
5. |19.5| =
6. |-3/4| =

Part 3: Compare the Values

Fill in the blank circle with <, >, or = to make the statement true.

1. |-15| ◯ |15|
2. |-20| ◯ 19
3. 8 ◯ |-9|
4. |-5| + |3| ◯ |-8|
5. |12 - 7| ◯ |-5|
6. |-100| ◯ |50| + |50|

Part 4: Solving for a Variable

Find all possible values for x in the equations below. Hint: There might be more than one answer for some questions!

1. |x| = 22
2. |x| = 5
3. |x| = -10
4. |x| + 3 = 14

Part 5: Brain Challenge!

Read the scenario and answer the question.

A submarine is exploring the ocean. It starts at sea level (0 meters). It first descends to -150 meters. Later, it ascends to a position of -95 meters. At which point, -150 m or -95 m, was the submarine farther from sea level?

Answer:

Answer Key

Part 2: Find the Value

1. 12
2. 35
3. 0
4. 250
5. 19.5
6. 3/4

Part 3: Compare the Values

1. |-15| = |15| (15 = 15)
2. |-20| > 19 (20 > 19)
3. 8 < |-9| (8 < 9)
4. |-5| + |3| = |-8| (5 + 3 = 8)
5. |12 - 7| = |-5| (|5| = |-5|, so 5 = 5)
6. |-100| = |50| + |50| (100 = 50 + 50)

Part 4: Solving for a Variable

1. x = 22 or x = -22
2. x = 5 or x = -5
3. No solution. (Absolute value can never be negative.)
4. First, subtract 3 from both sides: |x| = 11. So, x = 11 or x = -11

Part 5: Brain Challenge!

Answer: The submarine was farther from sea level at -150 meters.
Explanation: The distance from sea level (0) is found by taking the absolute value. |-150| = 150 meters. |-95| = 95 meters. Since 150 > 95, the submarine was farther from the surface at -150 meters.