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|}}