How to Apply the Order of Operations

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed in a given expression. These rules are essential for performing mathematical operations correctly and consistently, as they ensure that everyone who solves the same problem gets the same answer.

The order of operations can be remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Each letter represents a category of operations that should be performed in order, from left to right, in any given expression.

Here is a step-by-step guide on how to apply the order of operations:

1. Evaluate any expressions inside parentheses first, starting with the innermost set of parentheses and working outward. If there are multiple sets of parentheses, evaluate them from the inside out.

2. Evaluate any exponents or roots next, from left to right. If there are multiple exponents or roots, evaluate them from left to right.

3. Perform any multiplication or division in the expression, from left to right. If there are multiple multiplication or division operations, evaluate them from left to right.

4. Perform any addition or subtraction in the expression, from left to right. If there are multiple addition or subtraction operations, evaluate them from left to right.

5. Repeat steps 1-4 until all operations in the expression have been evaluated.

It's important to remember that the order of operations is a convention that is universally accepted in mathematics. By following these rules, you can be sure that your mathematical expressions are being evaluated correctly and that your answers are consistent with those obtained by others who solve the same problem.