Removing a fraction in the denominator

Question

What steps do I need to take to simplify $\frac{1}{\frac{1}{\sqrt{2}}}$ to $\frac{\sqrt{2}}{1}$? Can you please explain the steps i need to take in this problem and explain generally how to remove fractions from the denominator.

Answer 1

It turns out that division is the same as multiplying something by its reciprocal. In this case, $\frac{1}{\frac{1}{\sqrt{2}}}=1\cdot\frac{\sqrt{2}}{1}=\sqrt{2}$, as desired. In general, to divide by a fraction, just multiply by the reciprocal.