# Key stage 3 maths:Understanding BIDMAS - The Order of Operations

February 24, 2014 by Mark Maclaine Mark Maclaine explains how to understand BIDMAS to make answering those GCSE and Key Stage 3 Maths questions a lot easier.

‘Order of operations’ is just a way of saying: if a sum has a lot of ‘operations’ (multiply, add, subtract etc), which one do you do first? It might seem not to matter, but it makes a huge difference to the answer! In some countries like the UK this is called “BIDMAS” or “BODMAS” and in the US it is called “PEMDAS”. Here’s what they stand for:

Brackets: (anything in brackets first)

Indices/Order: technical word for ‘powers and roots’ ie 32, √9 etc.

Division: ÷

Multiplication: ×

Subtraction:

Note: In the US system the first two letters stand for Parentheses, their word for brackets, and Exponents, what they call powers. One useful way of teaching this involves the following story. Imagine a market trader selling some cheap fruit. He sells 4 apples costing 5p each and an orange costing 10p. The buyer doesn’t have any money so the seller agrees to write it down.

4 × 5 + 10

The buyer thinks to himself: “That’s 4x5, which is 20p, then plus 10.”

The buyer comes back the next day and wants to pay. He brings 30p with him. However the shopkeeper says “No! That’s not it. Look:” he shows the man his notebook:

4 × 5 + 10

"See it’s 5+10, which is 15p, and then you multiply by 4. That’s 60p!" He says.

The buyer gets very annoyed. Now, who is right? If you’re reading this as a Maths tutor, why not try asking your students to imagine they are the shopkeeper, or the buyer, and argue for the order that they think is right.

Without knowing the order of operations, either of them could be right. If we know to do multiplication and division before doing any addition and subtraction, we can see that the buyer must be right: 4x5p gives you the cost of the apples (20p), and then adding 10p for the orange gives the total (30p).

Now imagine a different buyer buys one apple and one orange every day. She goes on holiday for four days and wants to buy fruit to last for her holiday. Now what should the sum be? Since an apple is 5p and an orange is 10p, we could still write the sum:

4 × 5 + 10

But this time, we need to do 5+10 for an orange and an apple, and then multiply that by 4, for the four days. So we add brackets.

4 × (5 + 10)

Now we can see that we need to do 5p+10p, which is 15p, and then multiply by 4 to make 60p.

Understanding BIDMAS, or the order of operations, is key to many areas of maths, including algebraic problems. See my post next week to see how to put it into practice.

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