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