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Maths blog - BODMAS Rule


I am sure you have heard the abbreviation “BODMAS” at least once in your life. I am also certain that it happened to be in a mathematics lecture. While to most of us, mathematics is a subject of fear, there are some formulae at our disposal that make it comparatively easier. One such example is the – BODMAS Rule. 

BODMAS has proven to be very handy while solving even the most complex mathematical expressions. As someone who has struggled with numbers, I found BODMAS to be a boon and it was responsible for me scoring decent marks in my school life. So, if you are in the same boat, don’t worry I’ve got you covered! And if you’re someone who takes pride in their mathematical skills, you should still read till the end because brushing up your skills is never a bad idea! 

So, let’s Begin! 

The rule or order that we use to simplify expressions in math is called BODMAS rule. Let’s see what it stands for. 

Very simply way to remember the BODMAS rule!

B — Brackets

O — Of (orders: Powers and radicals)

D — Division

M — Multiplication

A — Addition

S — Subtraction

 

BODMAS-Rule

 

 

 

 

 

 

 

Important Notes:

1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.

2. Division does not always come before multiplication. We must do one by one in the order from left to right.

3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right

Examples:

12 ÷ 3 x 5 = 4 x 5 = 20

13 – 5 + 9 = 8 + 9 = 17

In the above simplification, we have both division and multiplication. From left to right, we have division first and multiplication next. So, we do division first and multiplication next.

 

Solved Problems – BODMAS RULE

Problem 1:

Evaluate:  6 + 7 x 8

Solution:

Evaluation

 

= 6 + 7 x 8

= 6 + 56

= 62

Operation

 

Multiplication

Addition

Result

 

Problem 2:

Evaluate: 102 – 16 ÷ 8

Solution:

Evaluation

 

= 102 – 16 ÷ 8

= 100 – 16 ÷ 8

= 100 – 2

= 98

Operation

 

Power

Division

Subtraction


Result

 

 

Problem 3:

Evaluate: (25 + 11) x 2

Solution:

Evaluation

 

= (25 + 11) x 2

= 36 x 2

= 72

Operation

 

Bracket

Multiplication

Result

 

Problem 4:

Evaluate: 3 + 6 x (5 + 4) ÷ 3 -7

Solution:

Evaluation

 

= 3 + 6 x (5 + 4) ÷ 3 -7

= 3 + 6 x 9 ÷ 3 -7

= 3 + 54 ÷ 3 -7

= 3 + 18 -7

= 21 – 7

= 14

Operation

 

Bracket

Multiplication

Division

Addition

Subtraction

Result

 

Problem 5:

Evaluate: 56 – 2(20 + 12 ÷ 4 x 3 – 2 x 2) + 10

Solution:

Evaluation

 

= 56 – 2(20 + 12 ÷ 4 x 3 – 2 x 2) + 10

= 56 – 2(20 + 12 ÷ 4 x 3 – 2 x 2) + 10

= 56 – 2(20 + 3 x 3 – 2 x 2) + 10

= 56 – 2(20 + 9 – 4) + 10

= 56 – 2(29 – 4) + 10

= 56 – 2(25) + 10

= 56 – 50 + 10

= 6 + 10

= 16

Operation

 

Bracket

Division

Multiplication

Addition

Subtraction

Multiplication

Subtraction

Addition

Result

 

 

Problem 6:

Evaluate: 6 + [(16 – 4) ÷ (22 + 2)] – 2

Solution:

Evaluation

 

= 6 + [(16 – 4) ÷ (2+ 2)] – 2

= 6 + [12 ÷ (2+ 2)] – 2

= 6 + [12 ÷ (4 + 2)] – 2

= 6 + [12 ÷ 6] – 2

= 6 + 2 – 2

= 8 – 2

= 6

Operation

 

Square Bracket

Power

Bracket

Square Bracket

Addition

Subtraction

Result

 

Problem 7:

Evaluate: (96 ÷ 12) + 14 x (12 + 8) ÷ 2

Solution:

Evaluation

 

= (96 ÷ 12) + 14 x (12 + 8) ÷ 2

= 8 + 14 x 20 ÷ 2

= 8 + 280 ÷ 2

= 8 + 140

= 148

Operation

 

Bracket

Multiplication

Division

Addition

Result

 

Problem 8:

Evaluate: (93 + 15) ÷ (3 x 4) – 24 + 8

Solution:

Evaluation

 

= (93 + 15) ÷ (3 x 4) – 24 + 8

= 108 ÷ 12 – 24 + 8

= 9 – 24 + 8

= -15 + 8

= -7

Operation

 

Bracket

Division

Subtraction

Subtraction

Result

 

Problem 9:

Evaluate: 55 ÷ 11 + (18 – 6) x 9

Solution:

Evaluation

 

= 55 ÷ 11 + (18 – 6) x 9

= 55 ÷ 11 + 12 x 9

= 5 + 12 x 9

= 5 + 108

= 113

Operation

 

Bracket

Division

Multiplication

Addition

Result

 

Problem 10:

Evaluate: (7 + 18) x 3 ÷ (2 + 13) – 28

Solution:

Evaluation

 

= (7 + 18) x 3 ÷ (2 + 13) – 28

= 25 x 3 ÷ 15 – 28

= 75 ÷ 15 – 28

= 5 – 28= -23

Operation

 

Bracket

Multiplication

Division

Subtraction

Result

 

 

Hope these examples and the explanation regarding the BODMAS rule was beneficial to you.

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