- Resolve the expression within the first parentheses: \((8 \cdot 2) = 16\).
- Resolve the innermost parentheses within the brackets: \((3 \div 3) = 1\).
- Complete the division inside the brackets: \([2 \div 1] = 2\).
- Add the results together: \(16 + 2 = \boxed{18}\).
Explanation
- Understanding the Order of Operations
To simplify the expression \((8 \cdot 2) + [2 \div (3 \div 3)]\), we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This rule ensures that we evaluate expressions in a consistent, logical order. We start by resolving the expressions within the grouping symbols (parentheses and brackets).
- Evaluating the Grouped Expressions
First, look at the expression inside the parentheses: \((8 \cdot 2)\). Multiplying these gives us:
\[8 \cdot 2 = 16.\]
Next, focus on the expression within the brackets: \([2 \div (3 \div 3)]\). Inside these brackets, there is another set of parentheses \((3 \div 3)\), which must be resolved first:
\[3 \div 3 = 1.\]
Now substitute this back into the bracketed expression:
\[2 \div 1 = 2.\]
- Calculating the Final Result
Finally, we take the results from the previous steps and perform the final addition:
\[(8 \cdot 2) + [2 \div (3 \div 3)] = 16 + 2 = 18.\]
Thus, the expression simplifies to 18, confirming that option A is correct. The final value is \(\boxed{18}\).
Examples
In daily life, the order of operations is essential for consistent calculations, such as when preparing a budget or managing a recipe. Imagine you are buying two sets of items that cost \(\$8\) each, and you also need to split a \(\$2\) package of supplies equally between three people who are already sharing one supply each (represented as \(3 \div 3\)). Calculating your total cost involves precisely this type of grouping: \((8 \times 2) + (2 \div 1) = \boxed{\$18}\). Mastering this ensures you accurately track your expenses!