Which calculation would be done first to solve this expression?
$10 \times(16+8 \div 2)$
The order of operations is a set of rules used to ensure that mathematical expressions are evaluated in a consistent way. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). When evaluating the expression \(10 \times (16 + 8 \div 2)\), we must follow these priority rules to determine the correct sequence of operations.
The expression includes grouping symbols, specifically the parentheses \((16 + 8 \div 2)\). According to the rules, we must evaluate the contents of the parentheses first. Inside these parentheses, we encounter both addition (\(+\)) and division (\(\div\)). Following the order of operations, division must be performed before addition. Therefore, within the expression \((16 + 8 \div 2)\), the operation \(8 \div 2\) has higher priority than the addition of 16.
Comparing the given options:
Thus, the first calculation to be performed is \(8 \div 2\), making option C the correct choice.
Understanding the order of operations is essential in everyday life, especially in fields like computer programming or when calculating a household budget. For example, if you are calculating the total cost of an order where you have a discount applied to a subtotal of items plus a fixed shipping fee, the order of operations ensures you correctly multiply the items and add the shipping fee at the appropriate time to arrive at the correct final price. By following these rules, like the order \(\$100 + (2 \times \$5)\), we ensure that calculations are accurate and reliable.