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Dante took 5(1)/(2) hours to clean the bathroom. He took 3(2)/(5) hours to clean the bedroom. How much longer did it take Dante to clean the bathroom? Write your answer as a mixed number in simplest form.

Dante took 512 5 \frac{1}{2} hours to clean the bathroom. He took 325 3 \frac{2}{5} hours to clean the bedroom. How much longer did it take Dante to clean the bathroom?\newlineWrite your answer as a mixed number in simplest form.

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Full solution

Q. Dante took 512 5 \frac{1}{2} hours to clean the bathroom. He took 325 3 \frac{2}{5} hours to clean the bedroom. How much longer did it take Dante to clean the bathroom?\newlineWrite your answer as a mixed number in simplest form.
  1. Convert to Improper Fractions: Convert mixed numbers to improper fractions for easier calculation. \newline512=5×2+12=1125\frac{1}{2} = \frac{5\times 2 + 1}{2} = \frac{11}{2} hours.\newline325=3×5+25=1753\frac{2}{5} = \frac{3\times 5 + 2}{5} = \frac{17}{5} hours.
  2. Subtract Time Taken: Subtract the time taken to clean the bedroom from the time taken to clean the bathroom. \newline112−175=55−3410=2110\frac{11}{2} - \frac{17}{5} = \frac{55 - 34}{10} = \frac{21}{10} hours.
  3. Convert Back to Mixed Number: Convert the improper fraction back to a mixed number to answer the question. 2110=2110\frac{21}{10} = 2\frac{1}{10} hours.

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