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Difficulty: MediumOrder of Operations and Number Properties

If the mathematical expression below is simplified using the standard order of operations, what is the result?

12−6÷2×3+42 12 - 6 \div 2 \times 3 + 4^2
  1. A
    27
  2. B
    25
  3. C
    11
  4. 19Answer
  5. E
    -13

Answer

The correct result of the expression is 19.
The correct value is obtained by first evaluating the exponent (42=164^2 = 16), then performing the division and multiplication from left to right (6÷2=36 \div 2 = 3, followed by 3×3=93 \times 3 = 9), and finally performing the subtraction and addition from left to right (12−9=312 - 9 = 3, followed by 3+16=193 + 16 = 19).

Step-by-Step Solution

1
Evaluate the exponent term.
42=164^2 = 16
Exponents must be evaluated before multiplication, division, addition, and subtraction.
2
Perform multiplication and division from left to right.
6÷2×3=3×3=96 \div 2 \times 3 = 3 \times 3 = 9
Multiplication and division have equal precedence, so they are processed in order from left to right.
3
Perform addition and subtraction from left to right.
12−9+16=3+16=1912 - 9 + 16 = 3 + 16 = 19
Addition and subtraction have equal precedence, so they are processed in order from left to right.

Key Concept

Order of Operations (PEMDAS)
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Topics

Order of Operations and Number Properties

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