Find $\frac{25}{3} \cdot \frac{27}{300}$.
To multiply fractions, I can multiply the numerators and the denominators separately. So I have $\frac{25 \cdot 27}{3 \cdot 300}$. I can simplify this fraction by canceling out common factors in the numerator and denominator. I notice that 25 and 300 have a common factor of 25, so I can divide both by 25 and get 1 and 12 respectively. I also notice that 27 and 3 have a common factor of 3, so I can divide both by 3 and get 9 and 1 respectively. Now I have $\frac{1 \cdot 9}{1 \cdot 12}$. This simplifies to $\frac{9}{12}$. I can further simplify this fraction by dividing both the numerator and denominator by 3, since 3 is a common factor of 9 and 12. This gives me $\frac{3}{4}$. This is the simplest form of the fraction, so I'm done. 