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 :
|
Expression 6 + 7 x 8
|
Evaluation = 6 + 7 x 8 = 6 + 56 = 62 |
Operation Multiplication Addition Result |
Problem 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 |
Problem 3 :
Evaluate :
(25 + 11) x 2
Solution :
|
Expression (25 + 11) x 2 |
Evaluation = (25 + 11) x 2 = 36 x 2 = 72 |
Operation Bracket Multiplication Result |
Problem 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 Bracket Multiplication Division Addition Subtraction Result |
Problem 5 :
Evaluate :
36 - 2(20 + 12 ÷ 4 x 3 - 2 x 2) + 10
Solution :
Problem 6 :
Evaluate :
6 + [(16 - 4) ÷ (22 + 2)] - 2
Solution :
|
Expression 6+[(16-4)÷(22+2)]-2 |
Evaluation = 6+[(16-4)÷(22+2)]-2 = 6+[12÷(2²+2)]-2 = 6+[12÷(4+2)]-2 = 6+[12÷6]-2 = 6+2 - 2 = 8 - 2 = 6 |
Operation Bracket Power Parenthesis Parenthesis Addition Subtraction Result |
Problem 7 :
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 Bracket Multiplication Division Addition Result |
Problem 8 :
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 Bracket Division Subtraction Subtraction Result |
Problem 9 :
Evaluate :
55 ÷ 11 + (18 - 6) x 9
Solution :
|
Expression 55÷11+(18-6)x9 |
Evaluation = 55÷11+(18-6)x9 = 55÷11 + 12x9 = 5 + 12x9 = 5 + 108 = 113 |
Operation Bracket Division Multiplication Addition Result |
Problem 10 :
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 Bracket Multiplication Division Subtraction Result |