A pump currently contains 4 7/8 gallons of water but needs to be filled to capacity. The capacity of the pump is 9 5/8 gallons. How much more water is needed to completely fill the pump? Express your answer in simplest mixed-number form.

To calculate the water needed to completely fill the pump, subtract total capacity of the pump minus the current water contained in the pump . Since 9 5/8 gallons of water is the full capacity of the tank and 4 7/8 gallons of water were filled already, subtract 9 5/8 gallons of water by  4 7/8 gallons of water to get the water that is needed to completely fill the pump. To subtract mixed numbers, convert them first into improper fractions.
9 5/8 becomes 77/8 because the denominator 8 multiplied by the whole number 9 plus the numerator 5 is 77/8.
4 7/8 becomes 39/8 because the denominator 8 multiplied by the whole number 4 plus the numerator 7 is 39/8.
> 9 5/8 - 4 7/8
> 77/8- 39/8
> 38/8 
Simplifying to the lowest term;
> 38/8
> 19 *2/4*2
> 19/4.
Converting into a mixed number;
> 19/4 = 4 3/4.
4 3/4 gallons of water is needed to completely fill the pump.