Order of Operations
(KS2, Year 4)

The Lesson

The order of operations tells us what order to perform operations in. A calculation may have several operations, such as: adding, subtracting, multiplying, dividing and squaring.

Why Do We Need the Order of Operations?

Imagine we wanted to find the answer to the calculation below:

order of operations example This calculation contains two operations: adding and multiplying. There are two orders to doing this calculation and two answers. Do we add then multiply, or multiply then add?

Order 1

Add the first two numbers, then multiply the result with the third number.
1 + 2 × 3 = 3 × 3 = 9

Order 2

Multiply the last two numbers, then add the result to the first number.
1 + 2 × 3 = 1 + 6 = 7
Which answer is the correct one? It turns out the second order of operations is the correct one. Luckily, there is a simple way to use the correct order.

BODMAS

BODMAS is an acronym for the order of operations. It stands for:

BODMAS The order of operations is read from top to bottom. The operations with a curly bracket ({) are on the same level, and can be performed in any order.
  • Brackets. Evaluate brackets first.
  • Order. Evaluate exponents (such as squares and square roots) second.
  • Division and Multiplication. Evaluate numbers that are divided and multiplied third.
  • Addition and Subtraction. Evaluate numbers that are added and subtracted fourth.

How to Use the Order of Operations

Using the order of operations is easy.

Question

Find 2 + 32 − (8 × 2) ÷ 2.

Step-by-Step:

1

Brackets. Evaluate expressions within brackets first. In our example, there is one pair of brackets: (8 × 2) = 16.

2 + 32 − (8 × 2) ÷ 2

= 2 + 32 − 16 ÷ 2

2

Order. Evaluate numbers with exponents second. In our example, there is one exponent: 32 = 9.

2 + 32 − 16 ÷ 2

= 2 + 9 − 16 ÷ 2

3

Division and Multiplication. Evaluate numbers that are divided and multiplied third. In our example, there is one division: 16 ÷ 2 = 8.

2 + 9 − 16 ÷ 2

= 2 + 9 − 8

4

Addition and Subtraction. Evaluate numbers that are added and subtracted fourth. In our example, there is one +'s and one −. Addition and subtraction take the same precedence, so it does not matter which order we do them in. We will do them left to right.
2 + 9 − 8 = 11 − 8 \(\:\:\:\:\:\:\:\:\:\:\:\:\) as 2 + 9 = 11
11 − 8 = 3

Answer:

2 + 32 − (8 × 2) ÷ 2 = 3

Lesson Slides

The slider below shows another real example of how to use the order of operations. In another example, there is a pair of brackets which contains a long expression that itself needs to use the order of operations.

Top Tip

BODMAS, BIDMAS, BEDMAS, PEMDAS

BODMAS is one acronym used to remember the order of operations, but different parts of the world will use different ones.
  • BODMAS is used in the United Kingdom and Australia. Sometimes BIDMAS is used, where I is for Indices rather than Ofor Order.
  • BEDMAS is used in Canada, where E is for Exponent. The words (Order, Indices, Exponents) are all different words for the same thing.
  • PEMDAS is used in the United States of America: Parentheses, Exponent, Multiplication, Division, Addition, Subtraction. Parentheses is another word for brackets. A useful memory device for PEMDAS is "Please Excuse My Dear Aunt Sally."

Note

What Is an Operation?

An operation takes values and calculates a new value from them. parts_of_operations_explained
  • The numbers operated upon are called operands.
  • The symbol which shows what type of operation is taking place is called the operator.
author logo

This page was written by Stephen Clarke.