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Difficulty: MediumOrder of Operations

Arrange the mathematical steps in the correct sequence to evaluate the following expression according to the standard order of operations (PEMDAS):

12−4×∣−5+23∣ 12 - 4 \times \left| -5 + 2^3 \right|
  1. 1Calculate the value of the exponent, 232^3
  2. 2Add −5-5 and the evaluated exponent
  3. 3Determine the absolute value of the sum
  4. 4Multiply the absolute value result by 44
  5. 5Subtract the resulting product from 1212

Answer

The correct sequence starts with evaluating the exponent inside the absolute value, followed by addition, resolving the absolute value, multiplication, and finally subtraction.
Following the standard order of operations (PEMDAS), operations inside grouping symbols are prioritized. The absolute value bars act as a grouping symbol. Inside, the exponent is evaluated first, then the addition. The absolute value is then applied to the result. Finally, outside the grouping symbol, multiplication takes precedence over subtraction.

Step-by-Step Solution

1
Evaluate the exponent inside the absolute value.
12−4×∣−5+8∣ 12 - 4 \times \left| -5 + 8 \right|
Exponents within grouping symbols (absolute value) must be evaluated first.
2
Perform the addition inside the absolute value.
12−4×∣3∣ 12 - 4 \times \left| 3 \right|
Complete the operations inside the grouping symbols.
3
Resolve the absolute value.
12−4×3 12 - 4 \times 3
The absolute value of 33 is 33.
4
Perform the multiplication.
12−12 12 - 12
Multiplication precedes subtraction.
5
Perform the subtraction.
0 0
Subtraction is the final remaining operation.

Key Concept

Order of Operations (PEMDAS)
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Topics

Order of Operations

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