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Order of operations

Why do we all stop at a red light and go at a green light? Traffic lights would work just as well if everyone stopped on a green light and went on red. So long as we all do the same thing the traffic light system works. Chaos reigns when we do not have an agreed system by which everyone obeys.


Before we look more closely at the agreed system we use, how many different answers can you find to these calculations if we didn’t obey any rules for order of calculations?

a) \(6 \div 2(1+2)\)
b) \(9 – 3 \div \frac{1}{3} + 1\)

Post your solutions below.


It is obvious that when we write a calculation we need to agree the order in which we perform the operations, so that that all reach the same answer. In this section of the course we will work through the agreed order of operations. Whilst the order has been agreed, unfortunately the acronym used to remember the order has not. Text books may use BIDMAS or BODMAS or even PEMDAS. They all mean the same:

BIDMAS: Brackets, Indices, Division and Multiplication, Addition and Subtraction

BODMAS: Brackets, Orders, Division and Multiplication, Addition and Subtraction

PEMDAS: Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction

We will use BIDMAS.

The next four steps explain the order in which operations are performed.


Most modern day calculators obey the order of operations rule. Some calculators, usually older models, do not obey the order of operations rules. They just perform the calculations as they are typed in from left to right. It is worth typing in the calculations above into your calculator, make a note of the answer given, and as you work through the next steps decide whether your calculator obeys the order of operation rules.

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This article is from the free online course:

Maths Subject Knowledge: Understanding Numbers

National STEM Learning Centre