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The order of operations is a fundamental concept in mathematics that dictates the sequence of calculations in an expression. It ensures accurate results by following a structured four-step process: addressing grouping symbols, evaluating exponents and roots, performing multiplication and division from left to right, and completing addition and subtraction in order. The PEMDAS rule serves as a mnemonic to help remember this sequence, which is crucial for simplifying both numerical and algebraic expressions correctly.

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## Importance of the Order of Operations

### Essential Principle in Mathematics

The order of operations is a fundamental principle in mathematics that establishes the correct sequence for performing operations within an expression

### Four-Step Process for Simplifying Expressions

Grouping Symbols

Grouping symbols, such as parentheses, brackets, and braces, must be addressed first in the four-step process for simplifying expressions

Exponents and Roots

Exponents and roots are evaluated after grouping symbols in the four-step process for simplifying expressions

Multiplication and Division, Addition and Subtraction

Multiplication and division are performed before addition and subtraction in the four-step process for simplifying expressions

### Use of PEMDAS Rule

The PEMDAS rule, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, helps students remember the order of operations

## Application of the Order of Operations

### Numerical Expressions

The order of operations is used to simplify numerical expressions accurately, ensuring correct results

### Algebraic Expressions

The order of operations is equally important when simplifying algebraic expressions, especially when evaluating them for specific values of variables

### Example of Evaluating an Algebraic Expression

The order of operations is applied to evaluate the expression 4 - x^2 × 3 for x = 6, resulting in the correct answer of -104

## Components of the Order of Operations

### Grouping Symbols

Grouping symbols, such as parentheses, brackets, and braces, are critical in the order of operations as they indicate the portions of an expression that must be computed first

### Exponents and Roots

Exponents and roots are evaluated after grouping symbols in the order of operations

### Multiplication and Division, Addition and Subtraction

Multiplication and division are performed before addition and subtraction in the order of operations

Algorino

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