Absolute Value
Absolute value is a Grade 7 math concept from Yoshiwara Intermediate Algebra representing the distance a number is from zero on the number line. The absolute value |x| is always non-negative, and students learn to evaluate expressions and solve simple absolute value equations.
Key Concepts
Property The absolute value of $x$ represents the distance from $x$ to the origin on the number line. Because distance is never negative, the absolute value is always non negative. It is defined piecewise: $$|x| = \begin{cases} x & \text{if } x \geq 0 \\ x & \text{if } x < 0 \end{cases}$$.
Examples To simplify $|3 8|$, first perform the operation inside the bars: $|3 8| = | 5|$. Then take the absolute value, which is $5$. In the expression $|3| |8|$, we evaluate each absolute value first: $3 8$. The result is $ 5$. This shows that $|a b|$ is not always the same as $|a| |b|$. To simplify $5 + 2| 4|$, we first evaluate the absolute value: $| 4| = 4$. The expression becomes $5 + 2(4) = 5 + 8 = 13$.
Explanation Absolute value essentially makes any number positive. It measures a number's distance from zero on a number line, and distance is always a positive concept. Whether a number is positive or negative, its absolute value is its positive counterpart.
Common Questions
What is absolute value?
Absolute value |x| is the distance from x to 0 on the number line. It is always non-negative: |5| = 5 and |-5| = 5.
How do you evaluate an absolute value expression like |-3 + 7|?
First simplify inside: -3 + 7 = 4. Then take the absolute value: |4| = 4.
What is the absolute value of zero?
|0| = 0. Zero is its own distance from itself.
How is absolute value used in real life?
Absolute value is used to represent distances, error margins, and differences where direction does not matter, such as the difference in temperature between two cities.