Grade: Grade 6 Subject: Mathematics Unit: Integers SAT: Algebra ACT: Math

Absolute Value

Learn what absolute value means and how to find the distance of any number from zero.

What is Absolute Value?

Absolute Value = Distance from Zero

The absolute value of a number tells you how far that number is from zero, without caring about direction.

Think about it like this: If you're standing at zero on a number line, the absolute value tells you how many steps it takes to reach a number - whether you go left (negative) or right (positive).

The Absolute Value Symbol

| number | = distance from zero

We write absolute value using vertical bars around the number.

Visualizing on a Number Line

Both -5 and 5 are the same distance from 0

-5 -4 -3 -2 -1 0 1 2 3 4 5 5 units 5 units
|-5| = 5 and |5| = 5

Key Facts About Absolute Value

  • Absolute value is always positive or zero - distance can't be negative!
  • Opposites have the same absolute value - |−7| = |7| = 7
  • The absolute value of zero is zero - |0| = 0
  • The bars work like grouping symbols - simplify inside first

Quick Examples

|8|
=
8
8 is 8 units from zero
|-8|
=
8
-8 is also 8 units from zero
|0|
=
0
Zero is 0 units from itself
|-25|
=
25
-25 is 25 units from zero

Real-World Uses of Absolute Value

🌡️

Temperature Difference

How far from freezing (0°) is the temperature?

|-15°C| = 15 degrees from freezing
🏦

Money Owed

How much do you owe, regardless of + or -?

|-$50| = $50 owed
🌊

Elevation

Distance from sea level (0 feet)

|-200 feet| = 200 feet below sea level
🎯

Accuracy

How far off is an estimate?

|guess - actual| = error
Easy Way to Remember: When you see absolute value bars, just ask: "How far from zero?" and make the answer positive!

Worked Examples

Let's work through several absolute value problems step by step.

Example 1: Basic Absolute Value

Find: |-12|
1
Ask: How far is -12 from zero?
-12 is 12 units to the left of zero on the number line.
2
The distance is always positive:
|-12| = 12
|-12| = 12

Example 2: Comparing Absolute Values

Which is greater: |-15| or |10|?
1
Find each absolute value:
|-15| = 15 (15 units from zero)
|10| = 10 (10 units from zero)
2
Compare:
15 > 10
|-15| > |10| because 15 > 10

Example 3: Absolute Value with Operations

Find: |−3| + |−7|
1
Find each absolute value separately:
|−3| = 3
|−7| = 7
2
Add the results:
3 + 7 = 10
|−3| + |−7| = 3 + 7 = 10

Example 4: Expression Inside Absolute Value

Find: |5 − 12|
1
Simplify inside the bars first:
5 − 12 = −7
2
Now find the absolute value:
|−7| = 7
|5 − 12| = |−7| = 7

Practice Problems

Try these absolute value problems!

Problem 1

|−20| = ?

Problem 2

Which is greater: |−9| or |7|?

Problem 3

|−4| + |−6| = ?

Problem 4

|8 − 15| = ?

Check Your Understanding: Absolute Value Challenge

Test your absolute value skills with this 6-question challenge!

Absolute Value Challenge

Score: 0 / 6
Question 1 of 6

Challenge Complete!

0/6

Next Steps

Key Takeaways:

  • Absolute value measures the distance from zero on a number line
  • Absolute value is always positive or zero - never negative
  • Opposite numbers have the same absolute value: |−5| = |5| = 5
  • Simplify inside the absolute value bars first, then find the distance
  • Practice identifying absolute values of everyday numbers
  • Think about real-world situations involving distance from zero
  • Move on to learn about integer operations in the next lesson!