# Order of Operation – PEMDAS – BODMAS rule

We already know how to add, subtract, divide or multiply numbers.

But what if there are multiple operation in single expression?

For example:
⟹ 4 + 3 x 2

This expression contain both addition and multiplication.

Which operation you will do first?

If you add the number first, you will get:

4 + 3 x 2

7 x 2

14

If you multiply first, you will get:

⟹ 4 + 3 x 2

⟹ 4 + 6

10

See you are getting different result for same expression, which is not possible.

So which one is correct?

In this post we will understand the rule of operation when multiple math symbols are given.

## What is Order of Operation?

In math, the calculation of addition, subtraction, multiplication or division is known as Operation.

Order of operation is basically a math rule which tells you which operation to solve in the complex math expression.

### PEMDAS rule

In USA, the rule is known as PEMDAS, where;

P ⟹ Parentheses

E ⟹ Exponents

MD ⟹ Multiplication & Division (left to right)

AS ⟹ Addition & Subtraction (left to right)

It means if math expression is given to you, then you will solve:

(1) Parenthesis first,

(2) then move on to solve Exponents (E)

(3) then Multiplication & Division

(4) and at the very end Addition & Subtraction

Note:
Multiplication and Division are given same priority.

When both Multiplication & Division are present, solve the ones which appears first from left side.

This concept will get clear in following examples.

### BODMAS Rule

In other countries like UK or India, the same rule is remembered by the name of BODMAS.

B ⟹ Brackets

O ⟹ Orders (Powers/Square Roots etc.)

D ⟹ Division

M ⟹ Multiplication

S ⟹ Subtraction

Both PEMDAS and BODMAS mean the same thing. It’s just that they have different names.

Let us understand the concept with the help of examples:

Example 01
Solve the expression, 3 x ( 2 + 7 )

Solution
According to PEMDAS rule, solve numbers in Parenthesis (or Bracket) first

⟹ 3 x ( 2 + 7 )

⟹ 3 x 9

Now do the multiplication.

⟹ 3 x 9

27

Hence, 27 is the right answer

Example 02
Solve the expression, 2 x 10 + 6

Solution
According to PEMDAS, solve multiplication first and then addition

2 x 10 + 6

20 + 6

Now do the addition

26

Hence, 26 is the solution

Example 03
⟹ 2 x 11 – 12 \div 2

Solution

According to PEMDAS, multiplication & division are to be solved first.

Remember multiplication & division are of equal importance in PEMDAS

⟹ 2 x 11 – 12 \div 2

⟹ 22 – 6

⟹ 16

Hence, 16 is the solution

Example 04
⟹ 35 \div 7 x 3

Solution
According to PEMDAS, division and multiplication are of equal importance.

In the above expression, both multiplication & division operation are there. In this case, just solve the equation from left side.

Hence, 15 is the solution

Example 05
Solve the below math expression
⟹ 8 x 3 \div 4 – 5

Solution
As per PEMDAS, solve multiplication & division first and then subtraction.

Hence, 1 is the right answer

Example 06
Solve the below expression
( 7 x 8 – 4) / (6 – 4)

Solution
According to PEMDAS, solve the parenthesis (bracket) first

Hence, 26 is the solution.

Example 07
Solve the expression.
\Longrightarrow 2^{2} \times (6-3) \

Solution
As per PEMDAS, do the following order for above calculation

⟹ solve parenthesis (brackets) first

⟹ solve exponents (powers)

⟹ then do the multiplication

Hence, 12 is the right answer

I hope the above concept is clear. Let us solve some questions for our practice.

Please do not just view the solution. Take out your pen and paper and attempt each of the questions given below.

## Order of Operation Worksheet

Given below are the question on order of operation. All the questions are to the standard of Grade 5 Math.

Each question is provided with solution for your reference.

(01) 4\ \div \ 2\ +\ 3\ \times \ 3\ \\\ \\

(a) 12
(b) 11
(c) 18
(d) 20

\Longrightarrow 4\ \div \ 2\ +\ 3\ \times \ 3

Solve division & multiplication first.

\\ \Longrightarrow 2\ +\ 9

Now complete the addition.

\Longrightarrow \ 11\\\ \\

Option (b) is the right answer

(02) 2^{2} \times \ ( 6-2) \\\ \\

(a) 10
(b) 15
(c) 18
(d) 16

\Longrightarrow \ 2^{2} \times \ ( 6-2)

Solve parenthesis, then exponents and then multiplication.

\Longrightarrow 2^{2} \ \times \ ( 4)\\\ \\ \Longrightarrow \ 4\ \times \ ( 4)\\\ \\ \Longrightarrow \ 16\\\ \\

Option (d) is the right answer

(03) 5\ +\ 7\ \times \ 2 \\\ \\

(a) 19
(b) 20
(c) 21
(d) 18

\Longrightarrow 5\ +\ 7\ \times \ 2

First do multiplication and then addition.

\Longrightarrow \ 5\ +\ 14\\\ \\ \Longrightarrow \ 19\\\ \\

Option (a) is the right answer

(04) 5^{2} \ \times \ 2^{3} \\\ \\

(a) 220
(b) 180
(c) 200
(d) 210

\Longrightarrow \ 5^{2} \ \times \ 2^{3}

First solve exponents and then multiplication.

\Longrightarrow \ 25\ \times \ 8\\\ \\ \Longrightarrow \ 200\

Option (c) is the right answer

(05) ( 5\ \times \ 3\ -5) \ \ \times \ ( 3\ +\ 2) \\\ \\

(a) 80
(b) 50
(c) 60
(d) 70

\Longrightarrow \ ( 5\ \times \ 3\ -5) \ \ \times \ ( 3\ +\ 2)

First solve both brackets and then multiply.

\Longrightarrow \ ( 15\ -5) \ \times \ ( 5)\\\ \\ \Longrightarrow \ ( 10) \ \times \ ( 5) \\\ \\ \Longrightarrow \ 50 \\\ \\

Option (b) is the right answer

(06) 8-16\ \div \ 2\ \times \ 3\ +\ 6

(a) -10
(b) 10
(c) -8
(d) 8

First solve division and multiplication part from left to right

Option (a) is the right answer

(07) 14\ \div \ 7\ +4\ +\ 3\ \times \ 3

(a) 19
(b) 10
(c) 14
(d) 15

As per PEMDAS, first do multiplication/division and then go for addition

Number 15 is the solution

Option (d) is the right answer

(08) -\ 3( 2\ \times 4\ -\ 3\div 3) \ +\ ( 4+2\ -1)

(a) 16
(b) -16
(c) 15
(d) -15

As per BODMAS rule, follow the below steps:

(a) Solve both parenthesis independently
(b) Then do the addition

Hence -16 is the solution
Option (b) is the right answer

(09) \left( 5^{2} \times 2\ +\ 3^{2}\right) \ -2^{3} \div 8

(a) 60
(b) 55
(c) 65
(d) 58

Hence, 58 is the right answer

Option (d) is correct

(10) ( 10\div 2-1)^{2} \ +\ ( 4\times 2)^{2}

(a) 75
(b) 85
(c) 80
(d) 90