Verified Answer :

  • Apply the order of operations by first evaluating the exponent: \(4^2 = 16\).
  • Perform division and multiplication sequentially from left to right: \(27 \div 3 = 9\), then \(9 \times 2 = 18\).
  • Complete the final addition: \(18 + 16 = 34\).
  • The final result matches option (a), so the answer is \(\boxed{34}\).

Explanation

  1. Order of Operations Analysis

To evaluate the expression \(27 \div 3 \times 2 + 4^2\), we must follow the standard order of operations, often abbreviated as PEMDAS or BODMAS. This rule dictates the sequence in which mathematical operations should be performed:

  1. Parentheses/Brackets
  2. Exponents/Orders
  3. Multiplication and Division (performed from left to right)
  4. Addition and Subtraction (performed from left to right)
  1. Evaluating the Exponent

First, we handle the exponentiation. The expression includes \(4^2\), which means \(4 \times 4 = 16\).
The expression now becomes:
\[27 \div 3 \times 2 + 16\]

  1. Executing Multiplication and Division

Next, we perform the multiplication and division steps from left to right.
First, we divide \(27\) by \(3\), which gives \(9\).
\[9 \times 2 + 16\]
Then, we multiply \(9\) by \(2\), which gives \(18\).
\[18 + 16\]

  1. Final Addition and Conclusion

Finally, we perform the addition:
\[18 + 16 = 34\]
Comparing our result with the given choices, we find that 34 corresponds to option (a).

Examples

The order of operations is essential in everyday life, especially in fields like finance and programming. For example, when calculating a budget with multiple discounts or taxes—such as calculating a final price like original_price - discount + tax—using the correct order of operations ensures you arrive at the right value. Understanding this process helps avoid errors in daily tasks, from grocery shopping to managing household expenses, ensuring accurate results every time.

Related Questions