Order of Operations

Definition

The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure consistent and unambiguous results. This term is crucial in the context of various mathematical topics, including fractions, exponents, and radical expressions.

5 Must Know Facts For Your Next Test

1. The order of operations is commonly remembered using the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
2. When working with fractions, the order of operations must be followed to ensure that the numerator and denominator are properly evaluated.
3. In the context of exponents and scientific notation, the order of operations is crucial for correctly simplifying and evaluating expressions.
4. When dividing radical expressions, the order of operations must be observed to properly simplify the expression and arrive at the correct solution.
5. Failure to follow the order of operations can lead to incorrect results, even in seemingly simple mathematical expressions.

Review Questions

• Explain how the order of operations is applied when simplifying a fraction that contains multiple operations.
  • When simplifying a fraction that contains multiple operations, the order of operations must be followed. First, any operations within the numerator or denominator, such as addition, subtraction, multiplication, or division, must be performed. Then, once the numerator and denominator have been simplified, the fraction can be evaluated as a whole. This ensures that the final result is accurate and consistent, regardless of the complexity of the original expression.
• Describe the role of the order of operations in evaluating expressions involving exponents and scientific notation.
  • The order of operations is crucial when working with expressions that contain exponents and scientific notation. First, any operations within the exponents must be performed, following the PEMDAS rule. Then, the resulting values can be used to evaluate the overall expression. This is particularly important in scientific notation, where the exponent represents the power of 10 and must be properly accounted for to ensure the correct magnitude of the final result.
• Analyze how the order of operations impacts the process of dividing radical expressions.
  • When dividing radical expressions, the order of operations must be carefully observed. First, any operations within the radicands, such as addition, subtraction, multiplication, or division, must be performed. Then, the resulting values can be used to evaluate the division operation. Failing to follow the order of operations can lead to incorrect results, as the simplification of the radicands may depend on the order in which the operations are performed.

Related terms

Parentheses: Symbols used to group operations and indicate the order in which they should be performed.

Exponents: Mathematical operations that involve raising a number or variable to a power.

Roots: The inverse operation of exponents, where a number is raised to a fractional power.