What Are the Order of Operations?

Order of Operations

The order of operations is a term used to describe the order in which mathematical equations should be completed based on the type of operations performed.

Mathematical operations include: adding, subtracting, multiplying, and dividing. They also include finding orders and roots and solving brackets to work out an equation.

Children will learn about the basic four operations (adding, subtracting, multiplying, and dividing) before learning more complicated concepts.

What is the Order of Operations?

The order of operations is the rules that tell us in which order we should solve a mathematical problem. They’re ordered as follows:

  1. Parenthesis
  2. Exponents
  3. Multiplication
  4. Division
  5. Addition
  6. Subtraction

This is the correct order to solve equations that include more than one operation.

How can I remember the Order of Operations?

You can remember each order of operation by using the popular mnemonics: PEMDAS, BIDMAS, BODMAS, or PMDAS.

It helps you know which order to add, subtract, multiply, divide, or handle the different operations within an equation.

PEMDAS – Please Excuse My Dear Aunt Sally

Each letter in PEMDAS stands for one of the six operations above, helping students remember what comes first when completing a mathematical problem.

It can help them remember whether to add, subtract, multiply, divide, etc., within an equation first. Then, they know which order to complete the rest of the operations in.

PMDAS – Pass My Dog A Spoon

PMDAS is the simplified version of PEMDAS. It’s used mostly by children in primary school who aren’t using exponents yet in mathematics.

  1. Parentheses
  2. Multiplication
  3. Division
  4. Addition
  5. Subtraction


BIDMAS and BODMAS are used interchangeably with PEMDAS, depending on where you live and what vocabulary you use to describe mathematical operations.

If you’re wondering what the difference is between the two, don’t panic! ‘Indices’ and ‘Order’ are two different ways of describing the same thing, so either will help you get the same correct answer.

  1. Brackets
  2. Indices
  3. Division
  4. Multiplication
  5. Addition
  6. Subtraction
  1. Brackets
  2. Order
  3. Division
  4. Multiplication
  5. Addition
  6. Subtraction

Why is learning the Order of Operations essential?

Without knowing the order of operations, learners will struggle to approach more complicated mathematical problems that contain different operations. For example, with the following sum: (2 × 9) + (8 ÷ 4).

The first order of operation is the brackets (or parentheses), so we need to solve that first, giving us 18 + (8÷4). Next, we’ll need to solve the division, giving us 18 + 2 and a final answer of 20.

However, without knowing the correct order, learners could come to various answers. By tackling the addition before the addition, for example, they’d come to a long (and incorrect) decimal answer. By using the order of operations rules, children will always know how to tackle these problems.

Where did the Order of Operations come from?

The first mention of a particular order of operation that needed to come first came with the advent of maths textbooks in the 1800s. However, among mathematicians, there was more of a common understanding of what came first rather than a ‘discovery’ of this order.

Ultimately, this understanding means that we don’t need to parenthesize (or place into brackets) every single part of a mathematical problem.

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