Order of Operations Rules

Understanding the Order of Operations is key in Pre-Algebra. Using the PEMDAS acronym helps you remember the sequence: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Following these rules ensures accurate calculations and simplifies complex expressions.

1. PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)

   • PEMDAS is an acronym that helps remember the order of operations.
   • Always perform calculations in the order specified by PEMDAS to avoid errors.
   • Operations within the same category (Multiplication/Division or Addition/Subtraction) are performed from left to right.

2. Solve operations inside parentheses first

   • Parentheses indicate which operations should be prioritized.
   • Always complete calculations within parentheses before moving on to other operations.
   • If there are nested parentheses, solve the innermost one first.

3. Evaluate exponents next

   • Exponents represent repeated multiplication and should be calculated after parentheses.
   • This step is crucial for simplifying expressions correctly.
   • Remember that an exponent applies only to the number it is directly attached to.

4. Perform multiplication and division from left to right

   • These operations are of equal priority; perform them in the order they appear from left to right.
   • Be careful not to skip any steps; each operation must be completed as it appears.
   • Multiplication and division can be thought of as inverse operations.

5. Perform addition and subtraction from left to right

   • Like multiplication and division, addition and subtraction are of equal priority.
   • Complete these operations in the order they appear from left to right.
   • This step finalizes the simplification of the expression.

6. Use brackets or parentheses to clarify the order of operations when needed

   • Brackets can help avoid confusion in complex expressions.
   • They can indicate which operations should be performed first, especially in lengthy calculations.
   • Always ensure that the use of brackets does not alter the intended order of operations.

7. Simplify fractions before performing other operations

   • Reducing fractions can make calculations easier and clearer.
   • Simplifying fractions helps to avoid large numbers and complex calculations later.
   • Always check if a fraction can be simplified before proceeding with other operations.

8. Treat the numerator and denominator of a fraction as separate expressions

   • Each part of a fraction can be simplified independently.
   • This approach can help clarify complex calculations involving fractions.
   • Always ensure that operations on the numerator and denominator follow the order of operations.