What Is the Order of Operations
What Is the Order of Operations?
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:
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:
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 + 3^{2} − (8 × 2) ÷ 2.
StepbyStep:
1
Brackets.
Evaluate expressions within brackets first.
In our example, there is one pair of brackets: (8 × 2) = 16.
2 + 3^{2} − (8 × 2) ÷ 2
= 2 + 3^{2} − 16 ÷ 2
2
Order.
Evaluate numbers with exponents second.
In our example, there is one exponent: 3^{2} = 9.
2 + 3^{2} − 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 + 3^{2} − (8 × 2) ÷ 2 = 3