Absolute Value Division Property

Question

Can I do that kind of thing? I am using this property $$\left |\frac{a}{b} \right| = \frac{|a|}{|b|}$$.

Answer 1

Absolutely. Since |x| will at most change the sign of x, we only need to check that the sign of both sides is the same.

By definition, $\left|\frac{a}{b}\right|\geq 0$ and since $|a|,|b|\geq 0$, so is $\frac{|a|}{|b|}$.