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