Operations with rational numbers Transitional Reasoning Download PDF

Questions

1. 1.

   In a physics laboratory, a two-pan balance scale is used to calibrate precision weights. On the left pan, a student places 4 identical brass cylinders each weighing $1\frac{2}{3}$ ounces and 3 identical aluminum cubes each weighing $\frac{3}{4}$ ounce. On the right pan, the student places 5 identical steel bearings each weighing $1\frac{1}{6}$ ounces. What additional weight must be placed on the right pan to bring the scale into perfect balance?

   • A) $3\frac{1}{12}$ ounces
   • B) $2\frac{5}{12}$ ounces
   • C) $1\frac{1}{4}$ ounces
   • D) $\frac{5}{6}$ ounce
2. 2.

   A school student council tracks its seasonal event finances in a central ledger, starting the semester with a debt balance of $-32\frac{3}{4}$ dollars. During a charity bake sale, the council collects $97\frac{1}{2}$ dollars in revenue, but immediately spends $\frac{3}{5}$ of this revenue on craft materials. Finally, an outstanding printing fee of $14\frac{5}{8}$ dollars is deducted from the account. What is the council's final financial balance, in dollars?

   • A) $-8\frac{3}{8}$ dollars
   • B) $57\frac{1}{8}$ dollars
   • C) $50\frac{1}{8}$ dollars
   • D) $8\frac{3}{8}$ dollars
3. 3.

   An autonomous underwater research vehicle starts at sea level with an elevation of 0 meters and begins a diving mission. In the first phase, it descends at a constant rate of $3\frac{1}{5}$ meters per minute for 15 minutes. In the second phase, an upward thermal plume carries the vehicle upward by $18\frac{3}{4}$ meters. Finally, thrusters drive the vehicle down an additional $12\frac{1}{2}$ meters to collect seabed samples. What is the vehicle's final elevation relative to sea level?

   • A) $-38\frac{1}{4}$ meters
   • B) $-43\frac{1}{2}$ meters
   • C) $-40\frac{1}{2}$ meters
   • D) $-41\frac{3}{4}$ meters