Introduction to Simplification (BODMAS)

Introduction to Simplification (BODMAS)

Simplification questions ask you to evaluate a long arithmetic expression quickly and correctly. The key is to follow the correct order of operations, remembered as BODMAS.

BODMAS order

1. B – Brackets: ( ), { }, [ ] — solve innermost first.
2. O – Orders / Of: powers, roots, and "of" (which means multiplication).
3. D – Division
4. M – Multiplication
5. A – Addition
6. S – Subtraction

Division and multiplication are done left to right; so are addition and subtraction.

Worked example

Question: Simplify 18 ÷ 3 × 2 + (8 − 3) × 4

Solution:

1. Brackets: (8 − 3) = 5 → 18 ÷ 3 × 2 + 5 × 4
2. Division/multiplication left to right: 18 ÷ 3 = 6; 6 × 2 = 12; 5 × 4 = 20
3. Addition: 12 + 20 = 32

Answer: 32

Analogy

Analogy: Getting dressed in the right order

Solving an expression is like getting dressed in the morning — the order matters:

• B – Brackets: first pick the clothes out of the cupboard (open the brackets).
• O – Of / Orders: put on the inner layer (powers, roots, "of").
• D & M – Division and Multiplication: shirt and trousers — do them left to right, whichever comes first.
• A & S – Addition and Subtraction: shoes and watch at the end — again left to right.

If you wear shoes before socks, the result is a mess. In the same way, 8 + 4 × 3 must be 8 + 12 = 20, not 12 × 3 = 36.