Answer
The result will be larger than the original fraction, but not necessarily larger than the proper fraction itself.
Work Step by Step
Proper fractions have a numerator that is smaller than the denominator, while improper fractions have a numerator that is greater than or equal to the denominator.
Since the numerator is smaller than the denominator in a proper fraction, the overall fraction must be less than $1$. This means that when one divides by a proper fraction, one is dividing by a number less than 1. Dividing by a number less than 1 means that the quotient must be greater than the original fraction (but not necessarily greater than the proper fraction itself).
For instance, assume that the original fraction is $\frac{a}{b}$ and that the improper fraction is $\frac{c}{d}$. Then the division results in:
$\displaystyle \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}*\frac{d}{c}\gt \frac{a}{b}$ (because $d\gt c$ in a proper fraction)
Since the numerator in the proper fraction is smaller than the denominator ($c\lt d$), the resulting fraction must be larger than the original fraction. However, the result is not necessarily larger than the proper fraction itself.
For example:
Original fraction: $\frac{1}{2}$, proper fraction: $\frac{3}{4}$:
$\displaystyle \frac{\frac{1}{2}}{\frac{3}{4}}=\frac{1}{2}*\frac{4}{3}=\frac{4}{6}=\frac{2}{3}$
$\frac{2}{3}\gt \frac{1}{2}$, but $\frac{2}{3}\lt \frac{3}{4}$
