Simplify the following:$$\frac{3}{\sqrt{27}}$$
To simplify this fraction, I want to rationalize the denominator, which means getting rid of the square root by multiplying by a clever form of 1. So I have: $$\frac{3}{\sqrt{27}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{3 \sqrt{3}}{3 \sqrt{3} \cdot \sqrt{3}} = \frac{3 \sqrt{3}}{9}$$ Now I can simplify the fraction by dividing both the numerator and the denominator by 3, the greatest common factor. So I get: $$\frac{3 \sqrt{3}}{9} = \frac{\sqrt{3}}{3}$$ And that's the simplest form of the fraction. 