Mathematics: Order of Operations (PEMDAS/BODMAS)

Introduction

• Order of operations, also known as the rules for evaluating mathematical expressions, ensures consistency in calculating results.
• Without a defined order, multiple interpretations and incorrect solutions could arise.

The Order (PEMDAS/BODMAS)

• The order of operations is often remembered by the acronyms PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).
• Both acronyms represent the same hierarchy of operations.

Parentheses/Brackets

• Parentheses or brackets indicate the operations enclosed should be performed first.
• Innermost parentheses are evaluated first, then outer parentheses.
• Operations within parentheses are treated independently of the rest of the expression.

Exponents/Orders

• Exponents (or orders) involve raising a base to a power—e.g., 2³.
• Calculations involving exponents are performed after parentheses, before multiplication and division.

Multiplication and Division

• Multiplication and division are performed from left to right in the expression.
• They have equal precedence in the order of operations.
• If both operations appear, perform them in order of their occurrence from left to right.

Addition and Subtraction

• Addition and subtraction are performed from left to right in the expression.
• They have equal precedence in the order of operations.
• If both operations appear, perform them in order of their occurrence from left to right.

Importance of the Order

• Following the correct order is crucial to obtaining the correct solution to a mathematical expression involving multiple operations.
• Incorrect order leads to incorrect results.

Examples

• 2 + 3 × 4 (Multiplication first) = 2 + 12 = 14
• (2 + 3) × 4 (Parentheses first) = 5 × 4 = 20
• 10 ÷ 2 × 5 (Left to right, order of division and multiplication) = 5 × 5 = 25
• 8 - 2 + 3 (Left to right subtraction and addition) = 6 + 3 = 9

Complex Expressions

• Expressions with nested parentheses or a mixed array of operators necessitate applying the order of operations sequentially until the solution is obtained.

Test your understanding of the order of operations in mathematics with this quiz on PEMDAS and BODMAS. Learn how parentheses and exponents impact calculations and ensure accurate interpretations. Perfect for reinforcing key arithmetic concepts.