BODMAS RULE

The rule or order that we use to simplify expressions in math is called BODMAS rule.

Very simply way to remember BODMAS rule!

B ----> Brackets

O ----> Of (orders :Powers and radicals)

D ----> Division

M ----> Multiplication

A ----> Addition

S ----> Subtraction

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 have to 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

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

Problem 11 :

Evaluate :

[11 - 20 ÷ (52 - 13) ÷ 3 + 8] x 2

Solution :

Evaluation

= [11 - 20 + (52 - 13) ÷ 3 x 8] x 2

[11 - 20 + (52 - 13) ÷ 3 x 8] x 2

[11 - 20 + (52 - 13) ÷ 3 x 8] x 2.

[11 - 20 + (25 - 13) ÷ 3 x 8] x 2

[11 - 20 + 12 ÷ 3 x 8] x 2

[11 - 20 + 4 x 8] x 2

[11 - 20 + 32] x 2

[-9 + 32] x 2

= 23 x 2

= 46

Operation

Bracket2

Bracket2

Exponent2

Bracket

Division

Multiplication

Subtraction

Bracket

Multiplication

Result

Problem 12 :

Evaluate :

a- (b2 + c) ÷ a + (ab + c)

if a = 4, b = -3 and c = 7.

Solution :

a- (b2 + c) ÷ a + (ab + c)

Substitute a = 4, b = -3 and c = 7.

4- [(-3)2 + 7] ÷ 4 + [4(-3) + 7]

Evaluation

= 4- [(-3)2 + 7] ÷ 4 + [4(-3) + 7]

= 4- [(-3)2 + 7] ÷ 4 + [4(-3) + 7]

= 4[9 + 7] ÷ 4 + [4(-3) + 7]

= 4- 16 ÷ 4 + [-12 + 7]

= 4- 16 ÷ 4 - 5

= 64 - 16 ÷ 4 - 5

= 64 - 4 - 5

60 - 5

= 55

Operation

Brackets2

Exponent2

Brackets2

2Bracket2

Exponent2

Division

Subtraction

Subtraction

Result

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