Order of operations Transitional Reasoning Download PDF

Questions

1. 1.

   A manufacturing plant uses two automated packaging lines, Line A and Line B, whose hourly production rates in boxes are programmed using mathematical expressions. Line A: $144 \div 6 \times 3 \div (4 \times 2 \div 4)$ Line B: $144 \div (6 \times 3) \times (8 \div 2 \div 2)$ Following the standard order of operations, how many more boxes per hour does Line A produce than Line B?

   • A) 12 boxes
   • B) 28 boxes
   • C) 32 boxes
   • D) 20 boxes
2. 2.

   A computer science student writes a diagnostic tool to demonstrate common calculation errors when applying the order of operations. The program evaluates the expression $72 \div 4 \times 3$ using the standard left-to-right rule for multiplication and division, and then re-evaluates it under the common mistaken rule where multiplication is given priority over division. What is the difference between the correct value calculated by the program and the value obtained using the mistaken rule?

   • A) 48
   • B) 42
   • C) 18
   • D) 6
3. 3.

   An automated manufacturing controller processes parts according to a mathematical formula programmed into its logic unit. A technician discovers that without grouping symbols, the expression $48 \div 2 \times 3 + 5$ yields a value of 77, but the machine requires a calibrated target output of 13 to function safely. Which placement of a single pair of parentheses achieves the required output of 13?

   • A) $(48 \div 2) \times 3 + 5$
   • B) $48 \div 2 \times (3 + 5)$
   • C) $48 \div (2 \times 3 + 5)$
   • D) $48 \div (2 \times 3) + 5$
4. 4.

   An environmental monitoring station records hourly air-quality adjustments using an automated sensor algorithm. At the end of a shift, the central processor evaluates the adjustment expression $40 + 60 \div 5 \times 3 - (14 + 6 \div 2)$ to determine the net index score. Following the standard order of operations, what is the final value computed by the processor?

   • A) 27
   • B) 43
   • C) 66
   • D) 59
5. 5.

   A science lab technician prepares testing solutions by diluting concentrated chemicals according to a precise protocol. To determine the volume of distilled water in milliliters needed for the mixture, the technician evaluates the expression $72 \div 6 \times 2 + 8 \times (5 - 2)$. Following the standard order of operations, what is the value of this expression?

   • A) 30
   • B) 48
   • C) 64
   • D) 96