Order of Operations (PEMDAS)

Understanding the Order of Operations (PEMDAS) is essential in Elementary Algebra. It helps you tackle complex expressions accurately by prioritizing calculations, ensuring you solve problems correctly and efficiently. Mastering this concept lays the groundwork for more advanced math skills.

1. Parentheses: Solve operations inside parentheses first

   • Always start with calculations inside parentheses to ensure accuracy.
   • Parentheses indicate which operations should be prioritized.
   • If there are multiple sets of parentheses, solve the innermost first.

2. Exponents: Evaluate exponents and roots

   • Exponents represent repeated multiplication of a number by itself.
   • Calculate exponents after resolving parentheses but before multiplication and division.
   • Roots (like square roots) are also considered exponents and should be evaluated at this stage.

3. Multiplication and Division: Perform 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 operations; each must be addressed as it appears.
   • Multiplication and division can be thought of as inverse operations.

4. Addition and Subtraction: Perform from left to right

   • Like multiplication and division, these operations are also of equal priority.
   • Address them in the order they appear from left to right.
   • Ensure that you do not confuse the order; follow the sequence strictly.

5. Brackets and braces: Treat as parentheses, solving innermost first

   • Brackets [ ] and braces { } serve the same purpose as parentheses ( ).
   • Always solve the innermost brackets or braces first before moving outward.
   • This helps maintain clarity in complex expressions.

6. Fraction bars act as grouping symbols

   • A fraction bar indicates that the numerator and denominator should be treated as separate groups.
   • Solve operations in the numerator and denominator independently before dividing.
   • This is crucial for maintaining the integrity of the fraction.

7. Simplify before solving when possible

   • Look for opportunities to simplify expressions before performing calculations.
   • Reducing fractions or combining like terms can make calculations easier.
   • Simplification can help prevent errors in more complex problems.

8. Use parentheses to clarify order in complex expressions

   • Adding parentheses can help clarify the intended order of operations in complicated expressions.
   • They can prevent misinterpretation and ensure that calculations are performed correctly.
   • Always consider using parentheses to enhance readability and accuracy in your work.