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Question

Difficulty: MediumOrder of Operations

Evaluate each of the following arithmetic expressions. Then, arrange the expressions in order from the smallest resulting value to the largest resulting value.

  1. 110−2×(4−1)210 - 2 \times (4 - 1)^2
  2. 210−(2×4)−1210 - (2 \times 4) - 1^2
  3. 310−2×4−(−1)310 - 2 \times 4 - (-1)^3
  4. 4(10−2)×4−12(10 - 2) \times 4 - 1^2

Answer

The correct sequence from smallest to largest is: 10−2×(4−1)210 - 2 \times (4 - 1)^2, 10−(2×4)−1210 - (2 \times 4) - 1^2, 10−2×4−(−1)310 - 2 \times 4 - (-1)^3, and (10−2)×4−12(10 - 2) \times 4 - 1^2.
Evaluating each expression using the correct order of operations yields -8, 31, 1, and 3 respectively. Arranging these integer values from smallest to largest dictates the correct order.

Step-by-Step Solution

1
Evaluate the first expression: 10−2×(4−1)210 - 2 \times (4 - 1)^2
−8-8
Applying PEMDAS: solve inside parentheses (3)(3), apply the exponent (32=9)(3^2 = 9), multiply (2×9=18)(2 \times 9 = 18), and subtract (10−18=−8)(10 - 18 = -8).
2
Evaluate the second expression: (10−2)×4−12(10 - 2) \times 4 - 1^2
3131
Applying PEMDAS: solve inside parentheses (8)(8), apply the exponent (12=1)(1^2 = 1), multiply (8×4=32)(8 \times 4 = 32), and subtract (32−1=31)(32 - 1 = 31).
3
Evaluate the third expression: 10−(2×4)−1210 - (2 \times 4) - 1^2
11
Applying PEMDAS: multiply inside parentheses (8)(8), apply the exponent (12=1)(1^2 = 1), and subtract from left to right (10−8=2;2−1=1)(10 - 8 = 2; 2 - 1 = 1).
4
Evaluate the fourth expression: 10−2×4−(−1)310 - 2 \times 4 - (-1)^3
33
Applying PEMDAS: apply the exponent ((−1)3=−1)((-1)^3 = -1), multiply (2×4=8)(2 \times 4 = 8), and subtract from left to right (10−8=2;2−(−1)=3)(10 - 8 = 2; 2 - (-1) = 3).
5
Arrange the evaluated numbers from smallest to largest
−8<1<3<31-8 < 1 < 3 < 31
Comparing the integer values yields the final logical order of the respective expressions.

Key Concept

Evaluating arithmetic expressions sequentially by applying the correct order of operations (PEMDAS) and then sorting the numerical values.
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Topics

Order of Operations

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