Adding and subtracting with unlike denominators Transitional Reasoning Download PDF

Questions

1. 1.

   During a science investigation, a student monitors two identical graduated containers filled with water. Container X is initially filled to $\frac{5}{8}$ of its capacity, and Container Y is initially filled to $\frac{2}{3}$ of its capacity. Over several days, Container X loses $\frac{1}{6}$ of its capacity due to evaporation, while Container Y loses $\frac{1}{4}$ of its capacity. At the end of the investigation, how much more water, as a fraction of a container's capacity, remains in Container X than in Container Y?

   • A) $\frac{1}{12}$
   • B) $\frac{5}{24}$
   • C) $\frac{1}{24}$
   • D) $\frac{1}{8}$
2. 2.

   A student fitness club tracks weekly training goals toward a running milestone. During the first half of the week, Maya completes $\frac{2}{5}$ of her total goal on Tuesday and $\frac{3}{8}$ of her goal on Thursday. Leo aims to achieve the exact same combined fraction of the milestone by running $\frac{1}{4}$ of the goal on Friday and the remainder on Saturday. What fraction of the weekly goal must Leo complete on Saturday to match Maya's combined achievement?

   • A) $\frac{11}{40}$
   • B) $\frac{17}{40}$
   • C) $\frac{21}{40}$
   • D) $\frac{27}{40}$
3. 3.

   A carpenter uses a 2-meter wooden board to construct a custom display stand. For the base frame, she cuts a piece measuring $\frac{5}{6}$ meter, and for the top rail, she cuts a piece measuring $\frac{7}{9}$ meter. How many meters of the wooden board remain after cutting these two pieces?

   • A) $\frac{5}{18}$ meter
   • B) $\frac{11}{18}$ meter
   • C) $\frac{7}{18}$ meter
   • D) $\frac{13}{18}$ meter
4. 4.

   A robotics team programs an autonomous rover along a straight track during a field test. In the morning session, the rover moves forward $\frac{7}{8}$ kilometer and then reverses $\frac{1}{6}$ kilometer to calibrate its sensors. In the afternoon session, the rover travels forward an additional $\frac{2}{3}$ kilometer from its calibration position. What is the rover's final distance, in kilometers, from the starting point at the end of the test?

   • A) $\frac{7}{6}$ km
   • B) $\frac{5}{4}$ km
   • C) $\frac{35}{24}$ km
   • D) $\frac{11}{8}$ km
5. 5.

   An art student combines $\frac{3}{4}$ liter of blue paint and $\frac{2}{3}$ liter of yellow paint in a jar to create green paint. Later, the student uses $\frac{5}{6}$ liter of this mixture for a canvas project. How many liters of paint remain in the jar?

   • A) $\frac{5}{12}$ liter
   • B) $\frac{1}{2}$ liter
   • C) $\frac{7}{12}$ liter
   • D) $\frac{3}{4}$ liter