The order of operations is a set of rules that dictate the precise sequence in which operations should be performed in a mathematical expression. The steps of the order of operations, commonly referred to as PEMDAS, are as follows:
1. Parentheses: Simplify any expressions within parentheses first.
2. Exponents: Evaluate any exponentiation (raising numbers to powers).
3. Multiplication and Division: Perform any multiplication and division operations from left to right.
4. Addition and Subtraction: Perform any addition and subtraction operations from left to right.
It is important to follow the steps of the order of operations because they ensure that mathematical expressions are evaluated consistently and correctly. By strictly adhering to these steps, you can reach the correct result without any ambiguity.
Solving the problem from left to right, without following the order of operations, may lead to incorrect answers. This is because mathematical operations have different precedences, and ignoring these precedences can alter the outcome of the expression. For example, consider the expression 2 + 3 * 4. If you solve it from left to right, you would get 10, but according to the order of operations, the correct answer is 14. By following the steps systematically, you avoid confusion and ensure accurate results.