Moving denominator $x$ to numerator for algebra fraction

Question

For the question, $x=\frac{a}{{3b}}$, can the denominator of "$b$" be brought up to the numerator such that it becomes $x=\frac{a/b}{3}$ ? If not, what are the laws that I have to apply?

The question I am solving is $x=\frac{a}{b} = \frac{b}{a/3}$.

Answer 1

You can bring the b up by multiplying the top and bottom by 1/b. $a * \frac{1}{b} = a/b$, $3b * \frac{1}{b} = 3$, and putting it back together gives $\frac{a/b}{3}$. The only thing you need to make sure is that b is not 0, as $\frac{1}{0}$ would be undefined and it would be an invalid operation to multiply by it.