# Results of Absolute Value

Consider that $a,b \in \mathbb{R}$, then

1. $\left| a \right| \geqslant 0$ and $\left| a \right| = 0 \Leftrightarrow a = 0$

2. $\left| {a + b} \right| \leqslant \left| a \right| + \left| b \right|$

3. $\left| {a – b} \right| \geqslant \left| a \right| – \left| b \right|$

4. $\left| {ab} \right| = \left| a \right|\left| b \right|$

5. $\left| {\frac{a}{b}} \right| = \frac{{\left| a \right|}}{{\left| b \right|}}$