Often people are confused about which operation to carry out first. For example, you have an equation, 3 + 5 - 2 \div 1, apply operation is not a problem but the question is which one to carry out first? Is it the division, addition, or subtraction? If you are thinking the same then don't worry because, in this lesson, you will learn the order of operations.

Types of Combined Operations

There are so many ways of solving equations with different orders of operation. The problem is that with a different order, we get a different answer. We can't declare that answer wrong on the basis of the method. That is why mathematicians came up with a new rule of solving equations which is known as the BODMAS rule. Every word in BODMAS has a meaning, BO stands brackets off (without parentheses), it means that whatever is in the parentheses, you will solve that first. Same BODMAS rule will also be applied within the parentheses. D stands for Division which means that after solving parentheses, the next operation you need to apply is the division. The next one is multiplication which is the M in BODMAS and it means after solving the parentheses and division operation, it is time to go for the multiplication operation. The last two letters, A and S, stands for Addition and Subtraction. Since the letter A is before the letter S, that means you need to consider the addition operation first and then go for subtraction.

1. Operations without Parentheses

The best Maths tutors available
1st lesson free!
Intasar
4.9
4.9 (23 reviews)
Intasar
£42
/h
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£25
/h
1st lesson free!
Dr. Kritaphat
4.9
4.9 (6 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
Paolo
4.9
4.9 (11 reviews)
Paolo
£25
/h
1st lesson free!
Ayush
5
5 (28 reviews)
Ayush
£60
/h
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£27
/h
1st lesson free!
Rajan
4.9
4.9 (11 reviews)
Rajan
£15
/h
1st lesson free!
Farooq
5
5 (13 reviews)
Farooq
£35
/h
1st lesson free!
Intasar
4.9
4.9 (23 reviews)
Intasar
£42
/h
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£25
/h
1st lesson free!
Dr. Kritaphat
4.9
4.9 (6 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
Paolo
4.9
4.9 (11 reviews)
Paolo
£25
/h
1st lesson free!
Ayush
5
5 (28 reviews)
Ayush
£60
/h
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£27
/h
1st lesson free!
Rajan
4.9
4.9 (11 reviews)
Rajan
£15
/h
1st lesson free!
Farooq
5
5 (13 reviews)
Farooq
£35
/h
First Lesson Free>

1.1Additions and subtractions.

9 - 7 + 5 + 2 - 6 + 8 - 4 =

Starting from the left, carry out operations as they appear.

= 9 - 7 + 5 + 2 - 6 + 8 - 4 = 7

1.2 Additions, subtractions and multiplications.

3 \time 2 - 5 + 4 \time 3 - 8 + 5 \time 2 =

Carry out multiplications first, as they are higher priority.

= 6 - 5 + 12 - 8 + 10 =

Then, perform the additions and subtractions.

= 6 - 5 + 12 - 8 + 10 = 15

1.3 Additions, subtractions , multiplications and divisions.

10 \div 2 + 5 \times 3 + 4 − 5 \times 2 - 8 + 4 \times 2 − 16 \div 4 =

Perform the multiplications and divisions in the order in which they appear, as the two operations have the same priority.

= 5 + 15 + 4 - 10 - 8 + 8 - 4 =

Then, perform the additions and subtractions.

= 5 + 15 + 4 - 10 - 8 + 8 - 4 = 10

1.4 Additions, subtractions, multiplications, divisions and exponents.

{ 2 }^{ 3 } + 10 \div 2 + 5 \times 3 + 4 - 5 \times 2 - 8 + 4 \times { 2 }^{ 2 } - 16 \div 4 =

First, the powers have the highest priority.

= 8 + 10 \div 2 + 5 \times 3 + 4 - 5 \times 2 − 8 + 4 \times 4 - 16 \div 4 =

Continue with the multiplications and divisions.

= 8 + 5 + 15 + 4 - 10 − 8 + 16 - 4 =

Then, perform the additions and subtractions.

26

2. Operations with Parentheses

(15 - 4) + 3 - (12 - 5 \times 2) + (5 + 16 \div 4) -5 + (10 - { 2 }^{ 3 })=

First, calculate the values contained within the parentheses.

= [15 - (8 - 5 )] \times [5 + (6 - 4 )] - 3 + (8 - 6 ) =

Then, eliminate the parentheses making the operations.

= 11 + 3 - 2 + 9 - 5 + 2 = 18

3. Operations with Parentheses and Brackets

[15 - ({ 2 }^{ 3 } - 10 \div 2 )] \times [5 + (3 \times 2 - 4 )] - 3 + (8 - 2 \times 3 ) =

First, operate with the exponents, multiplications and divisions of the parentheses.

= (15 - (8 - 5 )] \times [5 + (6 - 4 )] - 3 + (8 - 6 ) =

Then, carry out the addition and subtraction of the parentheses.

= [15 - 3] \times [5 + 2 ] - 3 + 2 =

Instead of inserting brackets they are already in place:

= (15 - 3) \times (5 + 2) - 3 + 2=

Operate within the parentheses.

= 12 \times 7 - 3 + 2

Multiply.

= 84 - 3 + 2=

Subtract and add.

= 83

Need a Maths teacher?

Did you like the article?

1 Star2 Stars3 Stars4 Stars5 Stars 5.00/5 - 1 vote(s)
Loading...

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.