Question

Difficulty: MediumOrder of Operations and Number Properties

What is the value of the expression 3×(47)2+24234-3 \times (4 - 7)^2 + \frac{24}{2^3 - 4}?

  1. A
    8787
  2. B
    3333
  3. C
    15-15
  4. 21-21Answer
  5. E
    45-45

Answer

The correct answer is 21-21.
Following the order of operations, we first compute the term inside the parentheses: 47=34 - 7 = -3. Next, we evaluate the exponents: (3)2=9(-3)^2 = 9 and 23=82^3 = 8. This simplifies the expression to 3×9+2484-3 \times 9 + \frac{24}{8 - 4}. Simplifying the denominator gives 84=48 - 4 = 4. We then perform the multiplication and division: 3×9=27-3 \times 9 = -27 and 244=6\frac{24}{4} = 6. Adding these results together yields 27+6=21-27 + 6 = -21.

Step-by-Step Solution

1
Evaluate the subtraction inside the parentheses.
47=34 - 7 = -3
According to the order of operations, grouping symbols such as parentheses must be evaluated first.
2
Evaluate the exponential terms in the expression.
(3)2=9(-3)^2 = 9 and 23=82^3 = 8
Exponents must be evaluated after parentheses and before multiplication, division, addition, or subtraction.
3
Simplify the denominator of the fraction.
84=48 - 4 = 4
The denominator must be fully simplified before dividing the numerator by it.
4
Perform multiplication and division from left to right.
3×9=27-3 \times 9 = -27 and 244=6\frac{24}{4} = 6
Multiplication and division have higher priority than addition and subtraction.
5
Perform the final addition.
27+6=21-27 + 6 = -21
Addition and subtraction are performed last.

Key Concept

Order of Operations (PEMDAS)
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