Final answer:
In arithmetic expressions, the innermost set of parentheses should be evaluated first, following the order of operations known by the acronym PEMDAS. Start from the innermost parentheses and work outward to ensure correct sequence of calculations. The order of operations is vital for correct problem-solving in mathematics.
Step-by-step explanation:
When parentheses in an arithmetic expression are nested, the innermost set of parentheses is evaluated first. This rule is part of the order of operations in mathematics, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). When you encounter an expression with multiple levels of nested parentheses, start simplifying from the innermost pair and work your way outwards.
For example, in the expression (3 + (2 * (1 + 4))), the correct method is to first evaluate the expression within the innermost parentheses: (1 + 4), which equals 5. Next, you would multiply by 2 to get (2 * 5), which equals 10. Finally, you would add 3 to get the total of 13. This approach ensures that all calculations are performed in the correct sequence.
Remember that the order of operations is essential to correctly solving arithmetic problems. If you don't follow this order, you might end up with a different, incorrect result. It is a fundamental concept in mathematics and is critical for solving problems that include multiple operations and levels of nested parentheses.