A water botde holds \( 5 / 6 \) of a gallon of water. There are \( 62 / 3 \) gallons of water in a water tank. How many water bottles can be filled with the water in the tank? Write your answer as a fraction or as a whole or mixed number, water bottles

To find out how many water bottles can be filled with the water in the tank, we need to divide the total amount of water in the tank by the amount of water each bottle holds. 1. **Convert the gallons in the tank to an improper fraction:** \[ \frac{62}{3} \text{ gallons} \] 2. **Convert the amount of water each bottle holds to an improper fraction:** \[ \frac{5}{6} \text{ gallons} \] 3. **Divide the total gallons in the tank by the gallons per bottle:** \[ \text{Number of bottles} = \frac{\frac{62}{3}}{\frac{5}{6}} \] 4. **To divide fractions, multiply by the reciprocal:** \[ \frac{62}{3} \div \frac{5}{6} = \frac{62}{3} \times \frac{6}{5} \] 5. **Multiply the fractions:** \[ = \frac{62 \times 6}{3 \times 5} = \frac{372}{15} \] 6. **Simplify the fraction:** - Find the greatest common divisor (GCD) of 372 and 15. The GCD is 3. - Divide both the numerator and the denominator by 3: \[ \frac{372 \div 3}{15 \div 3} = \frac{124}{5} \] 7. **Convert the improper fraction to a mixed number:** - Divide 124 by 5: \[ 124 \div 5 = 24 \quad \text{(whole number)} \] - The remainder is: \[ 124 - (24 \times 5) = 124 - 120 = 4 \] - So, we can express this as: \[ 24 \frac{4}{5} \] Thus, the number of water bottles that can be filled with the water in the tank is: \[ \boxed{24 \frac{4}{5}} \text{ water bottles} \]