Adding and subtracting with unlike denominators Transitional Reasoning Practice

Questions

1. 1.

   A solar-powered irrigation battery begins the day fully charged. During the morning, water pumps consume $\frac{5}{12}$ of the full battery capacity, and during midday, solar panels recharge the battery by $\frac{1}{3}$ of its capacity. In the evening, the system uses an additional $\frac{3}{8}$ of the full battery capacity to distribute water across the fields. What fraction of the battery's full capacity remains at the end of the day?

   • A) $\frac{5}{24}$
   • B) $\frac{11}{24}$
   • C) $\frac{13}{24}$
   • D) $\frac{17}{24}$
2. 2.

   An artisan is cutting three fabric strips for a decorative wall hanging. The first strip is $\frac{7}{10}$ yard long. The second strip is $\frac{1}{6}$ yard shorter than the first strip, and the third strip is $\frac{3}{4}$ yard longer than the second strip. What is the length of the third fabric strip?

   • A) $\frac{47}{60}$ yard
   • B) $1\frac{9}{20}$ yards
   • C) $1\frac{37}{60}$ yards
   • D) $1\frac{17}{60}$ yards
3. 3.

   An engineering student is testing two model bridge designs, Truss A and Truss B, using lightweight wooden dowels. Truss A requires two dowels with lengths of $\frac{5}{6}$ meter and $\frac{3}{8}$ meter joined together. Truss B requires two dowels with lengths of $\frac{2}{3}$ meter and $\frac{1}{4}$ meter joined together. How much longer is the total length of dowels used for Truss A than the total length used for Truss B?

   • A) $\frac{1}{8}$ meter
   • B) $\frac{5}{24}$ meter
   • C) $\frac{1}{3}$ meter
   • D) $\frac{7}{24}$ meter
4. 4.

   Maya is training for a community triathlon and sets a goal to complete a total distance of $2\frac{1}{2}$ miles in one workout. During the first part of the session, she runs for $\frac{7}{8}$ mile and then cycles for $1\frac{1}{6}$ miles before taking a water break. How many more miles must Maya travel to reach her training goal?

   • A) $\frac{7}{24}$ mile
   • B) $\frac{11}{24}$ mile
   • C) $\frac{13}{24}$ mile
   • D) $\frac{17}{24}$ mile

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