We need to distribute 7/8 of a gallon into cups of 1/16 of a gallon. It means that to know the number of cups, we need to divide 7/8 into 1/16.
So, let's remember how to make a division between two fractions:
Then, the division of 7/8 into 1/16 is equal to:
Therefore, he gets 14 cups of blue paint.
Answer: 14 cups