Order of Operations

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Order of Operations in Mathematics

It’s easy to calculate an expression with only one mathematical operation. But what about when we have more than one mathematical operation how do we do the calculation so we can get the correct answer.

In mathematics we have presented some rules so we can follow to help us with the order of operations when we do calculations.

These rules are known as the “Order of Operations

We have named this order of operations with the word “BODMAS’’

BODMAS is an acronym that shows us the order we have to follow when we do calculations.

What does BODMAS mean?

order of operations

– Brackets (), [], {}, which means in an expression the first thing you have to do is the simplification of the brackets. We can remove brackets from an expression by expanding them by multiplications. In mathematics we first simplify the round brackets then the square brackets and lastly the curly one.

O – Of (orders, power and square, cube roots), which means you have to solve all the numbers which have powers and roots.

D – Division (which means you have to perform the division operation)

M – Multiplication (means that you have to perform the multiplication operation)

A – Addition (means that you have to perform the addition operation)

S – Subtract (means that you have to perform the subtraction operation)

Be Careful!
Division and Multiplication perform equally so calculate them from left to right side.
Addition and Subtraction perform equally so calculate them from left to right side.

Another way to name these orders of operations is the acronym PEMDAS and it’s used in the USA and means the same thing as BODMAS.

Examples using the ‘’BODMAS’’ rule

Example 1: 
Simplify 12⋅(5 + 3)

Step 1: Following the BODMAS rule we should remove the round brackets first by doing the operation inside the bracket.
12 ⋅ 8

Step 2: All it’s left to do is the multiplication operation and we get our answer.
12 ⋅ 8 = 96

Example 2:
Simplify 60 ÷ 2(10 + 5)

Step 1: Remove the round brackets first by doing the operation inside it.
60 ÷ 2(10 + 5) = 60 ÷ 2 x 15

Step 2: Do multiplication and division operation from left to right.
60 ÷ 2 x 15 = 30 x 15 = 450

Example 3:  

Simplify 12⋅[2 ⋅ (5 – 3)]

Step 1: Firstly remove the round brackets first by doing the operation inside it.

12⋅[ 2 ⋅ 2 ]

Step 2: Secondly remove the square brackets by doing the operation inside.

12 ⋅ 4

Step 3: Thirdly do the multiplication operation and we get our answer:

12 ⋅ 4 = 48

Example 4:

Simplify 20 : 2 – (12 : 2) ⋅ 5 ⋅ 32

Step 1: Firstly remove the round brackets by doing the division operation.
20 : 2 – 6  32

Step 2: Secondly find the power.
20 ÷ 2 – 6 ⋅ 5 ⋅ 9

Step 3: Thirdly do the multiplication and division operation from left to right.
20 ÷ 2 – 6 ⋅ 5 ⋅ 9 =
10 – 6 ⋅ 5 ⋅ 9 =
10 – 30 ⋅ 9 =
10 – 270 = -260

Example 5: 

Simplify 8 ÷ 2(3 + 1)

Step 1: Do the multiplication and division operation from left to right.

8 ÷ 2(3 + 1) =
8 ÷  2 ⋅ 4
4 ⋅ 4 = 16

Example 6: 

Simplify 27 ÷ 9 x (3)

Step 1: Do the multiplication and division operation from left to right.27 ÷ 9(3) =

27 ÷ 9 x (3) = 3 x (3) = 9

Be careful !
Don’t misunderstand with the fact we should do the round brackets first, because we have no operation inside the round brackets that need to be done. We just have to follow the division and multiplication operation from left to right side.

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