Pre-Algebra
Numbers and operations
Absolute value
20 practice questions
0 video lessons
Theory + worked examples
Absolute Value
California Pre-Algebra • Standard 6.NS.7c • Numbers & Operations
Absolute Value is a topic in Numbers & Operations in the California Common Core State Standards. It is aligned to Standard 6.NS.7c, which requires students to understand absolute value as distance from zero and evaluate it.
The absolute value \(|x|\) is the distance of a number from zero, so it is never negative.
Theory
The absolute value \(|x|\) is the distance of \(x\) from \(0\) on the number line.
Distance is never negative, so \(|x|\ge0\) and \(|{-5}|=|5|=5\).
Absolute value is distance from zero.
What absolute value means.
Definition:
\[|x|=\begin{cases}x & x\ge0\\ -x & x<0\end{cases}\]
Simplify inside the bars first.
How to find absolute value
- Simplify any operations inside the bars.
- Drop the sign to get the distance.
- The result is zero or positive.
- Compare distances if asked.
Example 1 — Evaluate
Find \(|-9|\).
Solution
Distance of \(-9\) from \(0\) is \(9\).
| \(|-9|\) | \(=\) | \(9\) |
Example 2 — Positive inside
Find \(|7|\).
Solution
Distance of \(7\) from \(0\) is \(7\).
| \(|7|\) | \(=\) | \(7\) |
Example 3 — With operations
Find \(|3-8|\).
Solution
Simplify inside first, then take the distance.
| \(|3-8|\) | \(=\) | \(|-5|=5\) |
Example 4 — Compare
Which is larger, \(|-6|\) or \(|4|\)?
Solution
\(|-6|=6\) and \(|4|=4\).
| \(6\) | \(>\) | \(4\) |
Common pitfalls
\(|x|\) is never negative.
Simplify inside first: \(|3-8|=5\), not \(|3|-|8|\).
\(|-5|=5\), the bars are not parentheses.
Frequently asked questions
What is absolute value?
The distance of a number from zero.
Can absolute value be negative?
No, it is always zero or positive.
What is \(|-9|\)?
\(9\).
Do I simplify inside the bars first?
Yes, before removing the sign.
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