Order of Operations in Math

Overview

This lecture explains the correct order of operations in mathematics using the BODMAS/BIDMAS acronym, with worked examples to illustrate each step.

Order of Operations (BODMAS/BIDMAS)

• BODMAS/BIDMAS helps remember the order: Brackets, Orders (Indices), Division, Multiplication, Addition, Subtraction.
• Brackets are solved first; do all operations inside them before anything else.
• Orders/Indices refer to powers (e.g., squaring or cubing numbers).
• Division and multiplication come next, performed left to right as they appear.
• Addition and subtraction are done last, also in left-to-right order.
• Do not perform all divisions before multiplications or all additions before subtractions; proceed left to right for these pairs.

Worked Example 1

• For an expression like 3 + (18 ÷ 6)² × 2, first solve inside brackets: 18 ÷ 6 = 3.
• Replace bracket with result: 3 + 3² × 2.
• Apply the order/index: 3² = 9.
• Next, multiply: 9 × 2 = 18.
• Finally, add: 3 + 18 = 21.

Worked Example 2

• When multiple brackets exist, start left to right.
• Example: ((4² - 6 × 2) ÷ (4 ÷ 2 × 4)) + 7.
• Solve inside the first bracket: 4² = 16, 6 × 2 = 12, 16 - 12 = 4.
• In the second bracket: 4 ÷ 2 = 2, 2 × 4 = 8.
• The new expression: 4² ÷ 8 + 7.
• 4² = 16.
• 16 ÷ 8 = 2.
• 2 + 7 = 9.

Common Pitfalls & Tips

• The most common mistake is forgetting to use the BODMAS/BIDMAS order.
• Always ask yourself which operation comes next as you simplify.

Key Terms & Definitions

• BODMAS/BIDMAS — Acronym for Brackets, Orders (Indices), Division, Multiplication, Addition, Subtraction.
• Order/Index — Raised number indicating powers (e.g., squared or cubed).

Action Items / Next Steps

• Practice applying BODMAS/BIDMAS to different equations.
• Remember to work left to right for division/multiplication and addition/subtraction.