What is 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 first (Parentheses)
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.
To have better understanding on BODMAS rule, let us look at some more examples.
Bodmas Rule  Examples
Example 1 :
Evaluate :
6 + 7 x 8
Solution :
Expression
6 + 7 x 8
Evaluation
= 6 + 7 x 8
= 6 + 56
= 62
Operation
Multiplication
Addition
Result
Example 2 :
Evaluate :
10²  16 ÷ 8
Solution :
Expression
10²  16 ÷ 8
Evaluation
= 10²  16 ÷ 8
= 100  16 ÷ 8
= 100  2
= 98
Operation
Power
Division
Subtraction
Result
Example 3 :
Evaluate :
(25 + 11) x 2
Solution :
Expression
(25 + 11) x 2
Evaluation
= (25 + 11) x 2
= 36 x 2
= 72
Operation
Parenthesis
Multiplication
Result
Example 4 :
Evaluate :
3 + 6 x (5 + 4) ÷ 3 7
Solution :
Expression
3 + 6 x (5+4) ÷ 3 7
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
Parenthesis
Multiplication
Division
Addition
Subtraction
Result
Example 5 :
Evaluate :
6 + [(16  4) ÷ (2² + 2)]  2
Solution :
Expression
6+[(164)÷(2²+2)]2
Evaluation
= 6+[(164)÷(2²+2)]2
= 6+[12÷(2²+2)]2
= 6+[12÷(4+2)]2
= 6+[12÷6]2
= 6+2  2
= 8  2
= 6
Operation
Parenthesis
Power
Parenthesis
Parenthesis
Addition
Subtraction
Result
Example 6 :
Evaluate :
(96 ÷ 12) + 14 x (12 + 8) ÷ 2
Solution :
Expression
(96÷12)+14x(12+8) ÷ 2
Evaluation
=(96÷12)+14x(12+8) ÷ 2
= 8 + 14x20 ÷ 2
= 8 + 280 ÷ 2
= 8 + 140
= 148
Operation
Parentheses
Multiplication
Division
Addition
Result
Example 7 :
Evaluate :
(93 + 15) ÷ (3 x 4)  24 + 8
Solution :
Expression
(93+15)÷(3x4)24+8
Evaluation
= (93+15)÷(3x4)24+8
= 108 ÷ 12  24 + 8
= 9  24 + 8
= 15 + 8
= 7
Operation
Parenthesis
Division
Subtraction
Subtraction
Result
Example 8 :
Evaluate :
55 ÷ 11 + (18  6) x 9
Solution :
Expression
55÷11+(186)x9
Evaluation
= 55÷11+(186)x9
= 55÷11 + 12x9
= 5 + 12x9
= 5 + 108
= 113
Operation
Parenthesis
Division
Multiplication
Addition
Result
Example 9 :
Evaluate :
(7 + 18) x 3 ÷ (2 + 13)  28
Solution :
Expression
(7+18)x3÷(2+13) 28
Evaluation
= (7+18)x3÷(2+13)28
= 25 x 3 ÷ 15  28
= 75 ÷ 15  28
= 5  28
= 23
Operation
Parentheses
Multiplication
Division
Subtraction
Result
Expression
6 + 7 x 8

Evaluation
= 6 + 7 x 8
= 6 + 56
= 62

Operation
Multiplication
Addition
Result

Expression
10²  16 ÷ 8

Evaluation
= 10²  16 ÷ 8
= 100  16 ÷ 8
= 100  2
= 98

Operation
Power
Division
Subtraction
Result

Expression
(25 + 11) x 2

Evaluation
= (25 + 11) x 2
= 36 x 2
= 72

Operation
Parenthesis
Multiplication
Result

Expression
3 + 6 x (5+4) ÷ 3 7

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
Parenthesis
Multiplication
Division
Addition
Subtraction
Result

Expression
6+[(164)÷(2²+2)]2

Evaluation
= 6+[(164)÷(2²+2)]2
= 6+[12÷(2²+2)]2
= 6+[12÷(4+2)]2
= 6+[12÷6]2
= 6+2  2
= 8  2
= 6

Operation
Parenthesis
Power
Parenthesis
Parenthesis
Addition
Subtraction
Result

Expression
(96÷12)+14x(12+8) ÷ 2

Evaluation
=(96÷12)+14x(12+8) ÷ 2
= 8 + 14x20 ÷ 2
= 8 + 280 ÷ 2
= 8 + 140
= 148

Operation
Parentheses
Multiplication
Division
Addition
Result

Expression
(93+15)÷(3x4)24+8

Evaluation
= (93+15)÷(3x4)24+8
= 108 ÷ 12  24 + 8
= 9  24 + 8
= 15 + 8
= 7

Operation
Parenthesis
Division
Subtraction
Subtraction
Result

Expression
55÷11+(186)x9

Evaluation
= 55÷11+(186)x9
= 55÷11 + 12x9
= 5 + 12x9
= 5 + 108
= 113

Operation
Parenthesis
Division
Multiplication
Addition
Result

Expression
(7+18)x3÷(2+13) 28

Evaluation
= (7+18)x3÷(2+13)28
= 25 x 3 ÷ 15  28
= 75 ÷ 15  28
= 5  28
= 23

Operation
Parentheses
Multiplication
Division
Subtraction
Result
