Dividing unit fractions and whole numbers Transitional Reasoning Download PDF

Questions

1. 1.

   An upholstery workshop has two separate rolls of trim, each measuring 3 meters in length. The first roll is cut entirely into pieces that are each $\frac{1}{6}$ meter long. The second roll is cut entirely into pieces that are each $\frac{1}{4}$ meter long. How many more pieces are obtained from the first roll than from the second roll?

   • A) 2
   • B) 6
   • C) 12
   • D) 30
2. 2.

   In an agricultural laboratory, a technician prepares two distinct liquid plant treatments. For Treatment A, 3 liters of mineral solution are poured into small vials that each hold $\frac{1}{4}$ liter. For Treatment B, a single vial containing $\frac{1}{4}$ liter of concentrated enzyme is distributed equally among 6 plant trays. How many vials are filled for Treatment A, and what fraction of a liter does each tray receive for Treatment B?

   • A) 12 vials for Treatment A, and $\frac{3}{2}$ liters for Treatment B
   • B) $\frac{3}{4}$ vial for Treatment A, and $\frac{1}{24}$ liter for Treatment B
   • C) 12 vials for Treatment A, and $\frac{1}{24}$ liter for Treatment B
   • D) $\frac{1}{12}$ vial for Treatment A, and 24 liters for Treatment B
3. 3.

   A science club is allocated $\frac{1}{5}$ of a school's greenhouse space to conduct plant experiments. The club members divide this allocated space equally among 3 research teams. One research team then divides its assigned section into 2 equal plots to test different soil mixtures. What fraction of the school's total greenhouse space does one of these soil test plots represent?

   • A) $\frac{1}{10}$
   • B) $\frac{1}{15}$
   • C) $\frac{2}{15}$
   • D) $\frac{1}{30}$
4. 4.

   A community swimming pool requires 8 kilograms of water treatment powder. The powder comes in pre-measured packets that each contain $\frac{1}{3}$ kilogram of powder. The facility manager already has 9 of these packets in storage. How many more packets of powder must the manager purchase?

   • A) 5 packets
   • B) 15 packets
   • C) 24 packets
   • D) 33 packets
5. 5.

   A baker uses 4 kilograms of flour to make flatbreads, where each flatbread requires $\frac{1}{3}$ kilogram of flour. The baker then divides a single $\frac{1}{2}$-kilogram packet of yeast equally among all the flatbreads that were made. What fraction of a kilogram of yeast is used for each flatbread?

   • A) $\frac{1}{6}$
   • B) $\frac{1}{8}$
   • C) $\frac{1}{12}$
   • D) $\frac{1}{24}$