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Unit Rate with Fractions - Pre Algebra

  1. A garden hose fills 25\frac{2}{5} of a swimming pool in 2252\frac{2}{5} hours. At this rate, what fraction of the pool can be filled in one hour?
    Answer: 16\frac{1}{6} of the pool per hour Convert 2252\frac{2}{5} to 125\frac{12}{5} hours. Find the unit rate: 25125=25×512=212=16\frac{\frac{2}{5}}{\frac{12}{5}} = \frac{2}{5} \times \frac{5}{12} = \frac{2}{12} = \frac{1}{6} of the pool per hour. Choice A shows the unreduced fraction form. Choice C results from multiplying the fractions instead of dividing. Choice D incorrectly inverts the entire calculation and gives an unrealistic answer.
  2. A printer uses 78\frac{7}{8} of an ink cartridge to print 1341\frac{3}{4} reports. How much of an ink cartridge is needed per report?
    Answer: 12\frac{1}{2} of a cartridge per report Convert 1341\frac{3}{4} to 74\frac{7}{4} reports. Find ink per report: 7874=78×47=48=12\frac{\frac{7}{8}}{\frac{7}{4}} = \frac{7}{8} \times \frac{4}{7} = \frac{4}{8} = \frac{1}{2} cartridge per report. Choice B simplifies to 12\frac{1}{2} but is presented in unreduced form to confuse students. Choice C inverts the division incorrectly. Choice D results from multiplying instead of dividing the fractions.
  3. A machine produces 3353\frac{3}{5} widgets in 45\frac{4}{5} of a minute. What is the production rate in widgets per minute?
    Answer: 4124\frac{1}{2} widgets per minute Convert 3353\frac{3}{5} to 185\frac{18}{5} widgets. Find the unit rate: 18545=185×54=184=92=412\frac{\frac{18}{5}}{\frac{4}{5}} = \frac{18}{5} \times \frac{5}{4} = \frac{18}{4} = \frac{9}{2} = 4\frac{1}{2} widgets per minute. Choice B results from incorrectly computing 185×45\frac{18}{5} \times \frac{4}{5}. Choice C comes from subtracting 45\frac{4}{5} from 3353\frac{3}{5}. Choice D represents an incorrect decimal conversion.
  4. A water pump can fill 58\frac{5}{8} of a tank in 1131\frac{1}{3} hours. At this constant rate, how many tanks can the pump fill in one hour?
    Answer: 1532\frac{15}{32} tank per hour Convert 1131\frac{1}{3} to 43\frac{4}{3} hours. Find the unit rate: 5843=58×34=1532\frac{\frac{5}{8}}{\frac{4}{3}} = \frac{5}{8} \times \frac{3}{4} = \frac{15}{32} tank per hour. Choice B incorrectly inverts the final answer. Choice C results from multiplying the fractions incorrectly (58×14\frac{5}{8} \times \frac{1}{4}). Choice D comes from incorrectly converting the mixed number to 53\frac{5}{3}.

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