Simplify $\frac{10a^3}{55a^2}$ when $a=3$.
I notice that this is a fraction involving powers of a variable, so I want to simplify it as much as possible before plugging in the value of $a$. To simplify a fraction, I can divide both the numerator and the denominator by any common factor they have. In this case, I see that both the numerator and the denominator are divisible by 5 and by $a^2$, so I can divide them by those factors to get $\frac{10a^3}{55a^2} = \frac{2a}{11}$. Now that I have simplified the fraction, I can plug in $a=3$ and get $\frac{2a}{11} = \frac{2 \cdot 3}{11} = \frac{6}{11}$. 