Operations and Order

🎩 Imagine two mathematicians look at the same calculation: 3 + 4 × 2. One says the answer is 14, the other says 11. Who is right? They are both following different rules — but in mathematics, only ONE set of rules is accepted worldwide. That agreement is called BODMAS, and it tells every mathematician on the planet the exact order to tackle any calculation. Today you will master BODMAS, sharpen your long multiplication and long division, and use all four operations to crack multi-step problems like a professional.

BODMAS stands for Brackets, Order (powers and roots), Division, Multiplication, Addition, Subtraction. This is the agreed sequence for working through any calculation. Division and Multiplication share equal priority — you do whichever comes first reading left to right. The same applies to Addition and Subtraction. So in 3 + 4 × 2, you multiply first: 4 × 2 = 8, then add 3 to get 11. The person who got 14 added before multiplying — a very common mistake! Brackets override everything: (3 + 4) × 2 = 7 × 2 = 14, because the bracket is worked out first.

Now let us look at long multiplication — the formal written method for multiplying large numbers. To calculate 347 × 26, split 26 into 20 and 6. First multiply 347 × 6 = 2082. Then multiply 347 × 20 = 6940 (multiply by 2, then place a zero as a placeholder in the ones column). Finally add the two partial products: 2082 + 6940 = 9022. Always line up digits carefully in columns — ones under ones, tens under tens. This prevents costly errors and is the method used in formal examinations.

Long division uses a systematic process of divide, multiply, subtract, bring down — repeated until no digits remain. To calculate 852 ÷ 4: How many 4s in 8? → 2. Write 2 above. 2 × 4 = 8, subtract: 0 remainder. Bring down the 5. How many 4s in 5? → 1. Write 1. 1 × 4 = 4, subtract: remainder 1. Bring down the 2, making 12. How many 4s in 12? → 3. Write 3. Answer: 213. If a remainder is left at the end, it can be written as a fraction, decimal, or simply as R (remainder), depending on the context of the problem.

Multi-step problems combine all four operations and BODMAS together. Read the problem carefully and decide: what do I know? What do I need to find? What operations are needed and in what order? For example — a school orders 24 boxes of pencils, each holding 36 pencils. They give 150 pencils to Year 5 and share the rest equally among 6 classes. How many pencils per class? Step 1: 24 × 36 = 864 total. Step 2: 864 − 150 = 714 remaining. Step 3: 714 ÷ 6 = 119 per class. Writing each step separately avoids errors and gains full marks in assessments.

You have now covered three powerful tools: BODMAS to sequence mixed operations correctly, long multiplication to handle large numbers efficiently, and long division to share and group precisely. When these tools work together on multi-step problems, you can tackle almost any real-world calculation — from working out costs and quantities to analysing data. Always show your working step by step: it helps you spot mistakes, demonstrates your reasoning, and earns method marks in assessments. 🌟