Dividing fractions by fractions Transitional Reasoning Practice

Questions

1. 1.

   An agricultural research station evaluates an autonomous solar cultivator designed to aerate soil in greenhouse beds. During a continuous operational test, the cultivator aerates $\frac{7}{12}$ of a targeted test bed in $\frac{5}{6}$ of an hour. If the machine maintains this uniform rate of work, what fraction of the test bed can it aerate in one full hour?

   • A) $\frac{35}{72}$
   • B) $\frac{2}{3}$
   • C) $\frac{1}{4}$
   • D) $\frac{7}{10}$
2. 2.

   A civil engineering team is constructing an ecological water filtration pond with a rectangular surface. The planned surface area of the pond is $\frac{14}{25}$ square kilometer, and its surveyed width is $\frac{7}{10}$ kilometer. What is the length of this filtration pond, in kilometers?

   • A) $\frac{4}{5}$
   • B) $\frac{5}{4}$
   • C) $\frac{2}{5}$
   • D) $\frac{49}{125}$
3. 3.

   An environmental engineer tests two sustainable drainage pavements designed to absorb runoff during heavy rainfall. Under identical laboratory conditions, Pavement A absorbs $\frac{5}{12}$ cubic meter of water per minute, which is exactly $\frac{5}{8}$ of the volume absorbed per minute by Pavement B. Based on these test results, how many cubic meters of water does Pavement B absorb in one minute?

   • A) $\frac{25}{96}$
   • B) $\frac{2}{3}$
   • C) $\frac{3}{2}$
   • D) $\frac{25}{24}$
4. 4.

   A drone inspection team mapped $\frac{7}{12}$ of an agricultural reserve using $\frac{3}{8}$ of a single fully charged battery pack. If power consumption remains constant relative to the area covered, what fraction of a full battery pack is needed to map the entire reserve?

   • A) $\frac{14}{9}$
   • B) $\frac{7}{32}$
   • C) $\frac{9}{14}$
   • D) $\frac{5}{24}$
5. 5.

   A laboratory technician has $\frac{5}{6}$ liter of a liquid testing reagent. A standard soil contamination test requires exactly $\frac{2}{3}$ liter of this reagent. How many test portions can the technician prepare using the available reagent?

   • A) $\frac{5}{9}$
   • B) $\frac{4}{5}$
   • C) $\frac{5}{4}$
   • D) $\frac{9}{5}$

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