Fractions Transitional Reasoning Practice

Questions

1. 1.

   A logistics facility classifies shipping bins into three categories based on total mass: Light tier (less than $\frac{4}{9}$ kg), Standard tier ($\frac{4}{9}$ kg to $\frac{2}{3}$ kg, inclusive), and Heavy tier (greater than $\frac{2}{3}$ kg). An employee loads a bin with 11 sample packages, where each package has a mass equal to the unit fraction $\frac{1}{18}$ kg. Which category does this bin qualify for, and how does its mass compare to the category boundaries?

   • A) Light tier, because the total mass of $\frac{11}{18}$ kg is less than the lower boundary rewritten as $\frac{12}{18}$ kg.
   • B) Heavy tier, because the total mass of $\frac{11}{18}$ kg is greater than the upper boundary rewritten as $\frac{8}{18}$ kg.
   • C) Heavy tier, because the total mass of $\frac{11}{18}$ kg is greater than the upper boundary rewritten as $\frac{10}{18}$ kg.
   • D) Standard tier, because the total mass of $\frac{11}{18}$ kg falls between the boundary values rewritten as $\frac{8}{18}$ kg and $\frac{12}{18}$ kg.
2. 2.

   A quality control technician tests four automated dispensers—labeled W, X, Y, and Z—that release liquid solution into laboratory flasks. Dispenser W releases a volume composed of 8 unit fractions of size $\frac{1}{15}$ liter, Dispenser X releases $\frac{3}{5}$ liter, Dispenser Y releases $\frac{18}{30}$ liter, and Dispenser Z releases $\frac{2}{3}$ liter. Which pair of dispensers releases equivalent volumes, and what is the correct comparison of all four volumes from least to greatest?

   • A) Dispensers W and X release equivalent volumes, and the correct comparison from least to greatest is Dispenser Y < Dispenser W = Dispenser X < Dispenser Z.
   • B) Dispensers X and Y release equivalent volumes, and the correct comparison from least to greatest is Dispenser Z < Dispenser X = Dispenser Y < Dispenser W.
   • C) Dispensers X and Y release equivalent volumes, and the correct comparison from least to greatest is Dispenser W < Dispenser X = Dispenser Y < Dispenser Z.
   • D) Dispensers Y and Z release equivalent volumes, and the correct comparison from least to greatest is Dispenser W < Dispenser X < Dispenser Y = Dispenser Z.
3. 3.

   During a field test, four automated rovers navigate along identical straight test tracks. Rover 1 covers $\frac{5}{12}$ of its track, Rover 2 covers $\frac{4}{8}$ of its track, Rover 3 covers $\frac{3}{5}$ of its track, and Rover 4 covers $\frac{4}{9}$ of its track. An engineer needs to deploy a charging unit only to the rover that has completed more than half of its total track. Which rover receives the charging unit, and what is its distance expressed as an equivalent fraction with a denominator of 30?

   • A) Rover 1, with an equivalent fraction of $\frac{10}{30}$
   • B) Rover 2, with an equivalent fraction of $\frac{15}{30}$
   • C) Rover 3, with an equivalent fraction of $\frac{18}{30}$
   • D) Rover 4, with an equivalent fraction of $\frac{20}{30}$
4. 4.

   During a STEM workshop, students place indicator flags along identical 1-meter test tracks starting from 0 meters. Maya marks her track into 10 equal intervals and places a flag after 7 unit intervals, while Leo marks his track into 5 equal intervals and places a flag after 3 unit intervals. Tariq divides an identical track into 20 equal intervals and wants to place his flag at a location that lies strictly between Leo's flag and Maya's flag. Which fraction of a meter represents the position of Tariq's flag?

   • A) $\frac{11}{20}$ m
   • B) $\frac{13}{20}$ m
   • C) $\frac{15}{20}$ m
   • D) $\frac{17}{20}$ m
5. 5.

   On a straight 1-kilometer running path starting at 0 km, three students record their stopping points. Oliver stops at $\frac{5}{8}$ km, Lucas stops after covering 4 unit fractions of size $\frac{1}{6}$ km, and Chloe stops at $\frac{3}{4}$ km. Who stopped closest to the 1-kilometer finish mark, and which equivalent fraction with a denominator of 24 represents that person's location?

   • A) Chloe, because her location is equivalent to $\frac{18}{24}$ km
   • B) Lucas, because his location is equivalent to $\frac{16}{24}$ km
   • C) Oliver, because his location is equivalent to $\frac{15}{24}$ km
   • D) Chloe, because her location is equivalent to $\frac{12}{24}$ km

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