Simplification & BODMAS

Simplification & BODMAS

Concept Explanation

BODMAS is a simple rule that answers the age-old question: “but which one do I do first?” When you look at something like 5 + 3 × 2, most people instinctively want to add first and get 16, but the correct answer is actually 11 because multiplication comes before addition in the order of operations. BODMAS exists precisely to eliminate this ambiguity so everyone reading the same expression gets the same answer.

The acronym stands for Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction. But here’s where people trip up — Division and Multiplication are actually tied in priority, which means you do whichever one appears first as you read left to right. Same goes for Addition and Subtraction at the bottom of the ladder. It’s not that addition always comes after multiplication; it’s that multiplication always comes before addition.

Brackets are your superpower in simplification. Anything inside a bracket gets resolved completely before it touches the rest of the expression. And when you have nested brackets like (5 + (3 × (2 + 1))), you always crack the innermost one open first. Think of it like unwrapping layers of an onion — one layer at a time, from the inside out.

Key Formulas

Symbol	Meaning
()	Round brackets — innermost priority
{}	Curly brackets — middle priority
[]	Square brackets — outermost priority among brackets
a^b	Power/exponent — evaluate after brackets
÷ or /	Division — equal rank with multiplication
× or ·	Multiplication — equal rank with division
+	Addition — equal rank with subtraction
−	Subtraction — equal rank with addition

Step-by-Step Example

Q: Simplify: 20 ÷ 4 × 3 + (6 − 2)^2 − 5

Step 1: Solve brackets: (6 − 2) = 4 → 20 ÷ 4 × 3 + 4^2 − 5

Step 2: Solve orders (powers): 4^2 = 16 → 20 ÷ 4 × 3 + 16 − 5

Step 3: Division and Multiplication (left to right): 20 ÷ 4 = 5, then 5 × 3 = 15 → 15 + 16 − 5

Step 4: Addition and Subtraction (left to right): 15 + 16 = 31, then 31 − 5 = 26

Answer: 26

Common Mistakes

• Treating D and M as having strict order (division always before multiplication) → Correction: check left-to-right position, not alphabetical order
• Solving (a − b)^2 as a^2 − b^2 without expanding the bracket first → Correction: always expand brackets completely before applying any power
• Ignoring nested brackets and trying to solve them all at once → Correction: work from innermost bracket outward, one layer at a time

Quick Test (2 Qs)

1. Q: What is the value of 12 − 3 × 2 + 8 ÷ 4? Options: A) 10 B) 6 C) 8 D) 14 Ans: C) 8 (3 × 2 = 6, 8 ÷ 4 = 2, so 12 − 6 + 2 = 8)

2. Q: Simplify: [2 + (3 × 4 − 2)] ÷ 4 Options: A) 3 B) 4 C) 2.5 D) 3.5 Ans: A) 3 (innermost: 3 × 4 = 12, then 12 − 2 = 10, then 2 + 10 = 12, finally 12 ÷ 4 = 3)