Simplify:
$3 \cdot 3^2+8 \div 2-(4+3)$
A. 30
B. 23
C. 32
D. 24
Answer (1)
Evaluate the exponent: 3 2 = 9 .
Perform the multiplication: 3 ⋅ 9 = 27 .
Perform the division: 8 ÷ 2 = 4 .
Evaluate the parentheses: ( 4 + 3 ) = 7 .
Perform the addition and subtraction from left to right: 27 + 4 − 7 = 24 .
The simplified expression is 24 .
Explanation
Understanding the Problem We are asked to simplify the expression 3"." 3 2 + 8 ÷ 2 − ( 4 + 3 ) and select the correct answer from the given options. To do this, we need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Evaluating the Exponent First, we evaluate the exponent: 3 2 = 3 × 3 = 9 . So the expression becomes 3 ⋅ 9 + 8 ÷ 2 − ( 4 + 3 ) .
Performing Multiplication Next, we perform the multiplication: 3 ⋅ 9 = 27 . The expression is now 27 + 8 ÷ 2 − ( 4 + 3 ) .
Performing Division Then, we perform the division: 8 ÷ 2 = 4 . The expression becomes 27 + 4 − ( 4 + 3 ) .
Evaluating Parentheses Now, we evaluate the expression within the parentheses: ( 4 + 3 ) = 7 . The expression is now 27 + 4 − 7 .
Performing Addition Next, we perform the addition: 27 + 4 = 31 . The expression becomes 31 − 7 .
Performing Subtraction Finally, we perform the subtraction: 31 − 7 = 24 . Therefore, the simplified expression is 24.
Selecting the Correct Answer Comparing our result with the given options, we see that the correct answer is D. 24.
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating finances, measuring ingredients for a recipe, or determining project timelines. For instance, if you're calculating the total cost of items with discounts and taxes, following the correct order ensures you get an accurate final amount. This skill is fundamental for making informed decisions and avoiding errors in various practical situations.
