Mastering the Order of Operations: A Guide to Evaluating Mathematical Expressions Correctly

Order Of Operations

The order of operations, also known as PEMDAS, is a set of rules that dictate the order in which mathematical operations should be performed in an expression to ensure consistency and prevent ambiguity

The order of operations, also known as PEMDAS, is a set of rules that dictate the order in which mathematical operations should be performed in an expression to ensure consistency and prevent ambiguity. It helps to eliminate any confusion when evaluating complex mathematical expressions.

PEMDAS stands for:
1. Parentheses: Complete any calculations inside parentheses first.
2. Exponents: Perform any exponentiation or power calculations next.
3. Multiplication and Division: Perform any multiplication or division calculations from left to right.
4. Addition and Subtraction: Perform any addition or subtraction calculations from left to right.

Following this order ensures that the expression is evaluated correctly. Let’s look at an example to demonstrate how it works:

Expression: 5 + 4 * (6 – 2) / 2^2

1. Start with parentheses: (6 – 2) = 4.
The expression becomes: 5 + 4 * 4 / 2^2

2. Next, perform any exponentiation: 2^2 = 4.
The expression becomes: 5 + 4 * 4 / 4

3. Now, perform multiplication and division from left to right:
(4 * 4) = 16
The expression becomes: 5 + 16 / 4

4. Finally, perform addition and subtraction from left to right:
(16 / 4) = 4
The expression becomes: 5 + 4

Thus, the final result is 9.

Remember, following the order of operations is essential to ensure the correct evaluation of mathematical expressions. If you encounter nested parentheses or multiple operations of the same type, always work from the innermost parentheses or leftmost operation first.

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