Operations with rational numbers Transitional Reasoning Practice

Questions

1. 1.

   Two water filtration units, Unit P and Unit Q, are evaluated during a quality test. Unit P processes saline water at a rate of $3\frac{3}{4}$ liters per minute and discharges $\frac{1}{5}$ of the processed volume as wastewater, retaining the rest as purified water. Unit Q processes saline water at a rate of $4\frac{1}{6}$ liters per minute and discharges $\frac{3}{10}$ of the processed volume as wastewater, retaining the rest as purified water. If both units operate simultaneously for 10 minutes, how many more liters of purified water does Unit P produce than Unit Q?

   • A) $\frac{1}{12}$ liter
   • B) $\frac{5}{6}$ liter
   • C) $1\frac{1}{4}$ liters
   • D) $4\frac{1}{6}$ liters
2. 2.

   A robotic test cart moves along a straight calibrated track relative to a central sensor marked at $0$ meters. Starting at a position of $-2\frac{3}{5}$ meters, the cart travels forward in the positive direction at a constant speed of $\frac{3}{4}$ meters per second for $16$ seconds. It then reverses and travels in the negative direction a distance equal to $1\frac{1}{4}$ times its first positive displacement. Finally, an automated alignment shifts the cart forward in the positive direction by $1\frac{7}{10}$ meters. What is the cart's final position on the track relative to the sensor?

   • A) $1\frac{3}{10}$ meters
   • B) $-7\frac{3}{10}$ meters
   • C) $-3\frac{9}{10}$ meters
   • D) $-1\frac{3}{10}$ meters
3. 3.

   An artisan bakery begins the day with $48\frac{1}{2}$ kilograms of flour in storage. During the morning shift, the baker uses $5\frac{3}{4}$ kilograms of flour for each of 4 identical batches of bread, and in the afternoon, a shipment of $18\frac{5}{6}$ kilograms arrives and is added to the storage. Before closing, the baker uses $\frac{3}{7}$ of the total flour currently in storage to prepare pastries. How many kilograms of flour remain in storage at the end of the day?

   • A) $25\frac{1}{3}$ kg
   • B) 19 kg
   • C) $23\frac{1}{6}$ kg
   • D) $28\frac{2}{3}$ kg
4. 4.

   In a laboratory experiment, the initial temperature of a chemical solution is $-4\frac{1}{2}$°C. The solution is heated at a steady rate, increasing its temperature by $2\frac{3}{4}$°C each hour for 3 consecutive hours. At the end of the 3 hours, a stabilizer compound is introduced, which quickly lowers the temperature by $5\frac{1}{8}$°C. What is the final temperature of the solution in degrees Celsius?

   • A) $-1\frac{3}{8}$°C
   • B) $1\frac{3}{8}$°C
   • C) $-6\frac{7}{8}$°C
   • D) $3\frac{3}{4}$°C

Answers and step-by-step solutions appear after you finish the test.