Evaluate: $12+32 \div 8+10 \cdot 2^2$
Answer (1)
Evaluate the exponent: 2 2 = 4 .
Perform the division: 32 d i v 8 = 4 .
Perform the multiplication: 10 c d o t 4 = 40 .
Perform the addition: 12 + 4 + 40 = 56 .
The final answer is 56 .
Explanation
Understanding the Expression We need to evaluate the expression 12 + 32 d i v 8 + 10 c d o t 2 2 . To do this, we will follow the order of operations (PEMDAS/BODMAS), which tells us to evaluate exponents first, then multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Evaluating the Exponent First, we evaluate the exponent: 2 2 = 4 . So our expression becomes 12 + 32 d i v 8 + 10 c d o t 4 .
Performing the Division Next, we perform the division: 32 d i v 8 = 4 . Now our expression is 12 + 4 + 10 c d o t 4 .
Performing the Multiplication Now, we perform the multiplication: 10 c d o t 4 = 40 . The expression is now 12 + 4 + 40 .
Performing the Addition Finally, we perform the addition from left to right: 12 + 4 + 40 = 16 + 40 = 56 .
Final Answer Therefore, the value of the expression 12 + 32 d i v 8 + 10 c d o t 2 2 is 56 .
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating expenses or determining the outcome of a series of actions. For instance, if you're calculating the total cost of items with discounts and taxes, you need to apply the discount before adding the tax. Similarly, in programming, the order in which operations are performed can significantly affect the result. This problem reinforces the importance of following the correct sequence to arrive at the correct answer.
