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2.2: Absolute Value

  • Page ID
    41234
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    Every real number can be represented by a point on the real number line. The distance from a number (point) on the real line to the origin (zero) is what we called the magnitude (weight) of that number in Chapter 1. Mathematically, this is called the absolute value of the number. So, for example, the distance from the point −5 on the number line to the origin is 5 units.

    clipboard_ec4b2b7f02c327b4a2b45a54e36c5c1ae.png

    So is the distance from 5 to 0. Algebraically we can represent the absolute value as

    \[|x|=\left\{\begin{aligned}
    -x & \text { if } x<0 \\
    0 & \text { if } x=0 \\
    x & \text { if } x>0
    \end{aligned}\right.\nonumber\]

    Example B.1

    Evaluate each expression:

    1. \(|7|=7\)
    2. \(|-7|=7\)
    3. \(\left|\frac{-1}{4}\right|=\frac{1}{4}\)
    4. \(|-3|+|2|=3+2=5\)
    5. \(|-3+2|=|-1|=1\)
    6. \(|3|-|2|=3-2=1\)
    7. \(\frac{|-16|}{|-4|}=\frac{16}{4}=4\)
    8. \(\frac{-|7|-|-5|}{-|-3|}=\frac{-7-5}{-3}=\frac{-12}{-3}=4\)
    9. \(10 \cdot \frac{\left|3^{2}-3\right|}{4}+2=10 \cdot \frac{|9-3|}{4}+2=10 \cdot \frac{|6|}{4}+2=10 \cdot \frac{6}{4}+2=\not 2 \cdot 5 \cdot \frac{6}{\not 2 \cdot 2}+2=5 \cdot \frac{6}{2}+2=5 \cdot 3+2=15+2=17\)

    Note In relation to the order of operations PE(MD)(AS), the absolute value symbol is treated as a parenthesis, and so, what is inside has the priority over other operations.


    This page titled 2.2: Absolute Value is shared under a CC BY-NC-ND 4.0 license and was authored, remixed, and/or curated by Samar ElHitti, Marianna Bonanome, Holly Carley, Thomas Tradler, & Lin Zhou (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform.