To find the unit rate of flowers per vase, you divide the total number of flowers by the total number of vases.
Gloria has 112 flowers and 14 vases.
\[ \text{Flowers per vase} = \frac{112 \text{ flowers}}{14 \text{ vases}} = 8 \text{ flowers per vase} \]
Therefore, the unit rate is 8 flowers per vase.