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A company wishes to distill a 0.830 mole fraction ethanol (0.170 mole fraction water) solution. To aid in the distillation process, a 0.950 mole fraction benzene (0.050 mole fraction water) mixture containing fresh benzene and a recovered benzene solution is added.
An improper fraction is a fraction with a larger top than bottom, like 5 / 2. Mixed numbers are a whole number and a fraction together, like 2 1 / 2. It's usually easier to imagine 2 1 / 2 pizzas than five halves of a pizza, so it's useful to be able to switch between them.