Malone Global University

Lesson 01: Order of Operations (PEMDAS)

Use the standard hierarchy of operations to avoid ambiguity when simplifying expressions.

Course: Precalculus & Algebra • Unit: 1 • Lesson: 01

Objectives

  • Apply PEMDAS to evaluate expressions with integers and fractions.
  • Handle nested parentheses and exponents confidently.
  • Translate verbal descriptions into symbolic expressions.

Key Concepts

PEMDAS
Parentheses, Exponents, Multiplication/Division (L→R), Addition/Subtraction (L→R).
Left-to-right rule
When operations share priority, evaluate from left to right.

Worked Examples

Example A

Evaluate: \( 8 - 3^2 + 2\cdot 5 \)

Solution
  1. Exponents: \( 3^2 = 9\) ⇒ \( 8 - 9 + 10 \)
  2. Left-to-right addition/subtraction: \( (8 - 9) + 10 = -1 + 10 = 9 \)

Example B

Evaluate: \( 12\div(2\cdot 3) \)

Solution
  1. Parentheses first: \(2\cdot 3=6\)
  2. Then division: \(12\div 6=2\)

Practice

  1. \( 7 + 4\cdot 3 - 2^3 \)
  2. \( (5 - 2)^3 + 4\cdot 2 \)
  3. \( 18\div 3\cdot 2 - 4 \)
  4. \( 6[2 + 3(4 - 1)] \)
  5. \( \dfrac{2(3+5)}{4} + 1 \)