- Follow the standard order of operations (PEMDAS/BODMAS) starting with parentheses.
- Within the parentheses \((8.2 - 0.5 \times 7)\), perform multiplication before subtraction.
- The first operation is \(0.5 \times 7\).
- Final answer: \(\boxed{0.5 \times 7}\).
Explanation
- Analyzing the Order of Operations
To determine the first operation to perform, we use the standard order of operations, often abbreviated as PEMDAS/BODMAS. The rules for the order of operations are as follows:
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
The given expression is:
\[\frac{4.3 \times 3 + 11}{(8.2 - 0.5 \times 7) \div 6}\]
According to these rules, we must first address operations within the parentheses before moving to other parts of the expression. The expression inside the parentheses is \((8.2 - 0.5 \times 7)\).
- Identifying the First Operation
Within the parentheses \((8.2 - 0.5 \times 7)\), we must apply the order of operations again. We have a subtraction (\(8.2 - \dots\)) and a multiplication (\(0.5 \times 7\)). Multiplication has a higher priority than subtraction. Therefore, the multiplication operation \(0.5 \times 7\) must be calculated before the subtraction. Comparing this with the provided options, we can see that \(0.5 \times 7\) is the correct first operation to perform.
- Conclusion
By following the standard order of operations, we have determined that the multiplication \(0.5 \times 7\) inside the denominator's parentheses takes precedence over all other operations in the expression. Thus, the correct choice is the second option. The final answer is \(\boxed{0.5 \times 7}\).
Examples
Knowing the correct order of operations is essential for many daily tasks involving calculations. For example, if you are shopping and have a list of items with different unit prices, and there's a discount on some items, you need to calculate the discounts (multiplication) before subtracting them from the total (subtraction). Just like in our expression, failing to multiply first would lead to an incorrect total cost! Understanding these rules helps you manage budgets, build projects, and solve everyday math problems correctly.