Order of operations :
"Operations" means things like add, subtract, multiply, divide, squaring, etc.
When we have two or more operations in the same expression, we may have question about which one has to be done first, which one has to be done next.
But order of operations or bodmas rule or pemdas rule tells us in which order we have to do the operations one by one.
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 "Order of operations", let us look at some more examples problems.
Example 1 :
Evaluate : 6 + 7 x 8
Expression 6 + 7 x 8 |
Evaluation = 6 + 7 x 8 = 6 + 56 = 62 |
Operation Multiplication Addition Result |
Example 2 :
Evaluate : 10² - 16 ÷ 8
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
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
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 : 36 - 2(20+12÷4x3-2x2) + 10
Example 6 :
Evaluate : 6+[(16-4)÷(2²+2)]-2
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 Parenthesis Power Parenthesis Parenthesis Addition Subtraction Result |
Example 7 :
Evaluate : (96÷12)+14x(12+8)÷2
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 8 :
Evaluate : (93+15) ÷ (3x4) - 24 + 8
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 9 :
Evaluate : 55 ÷ 11 + (18 - 6) x 9
Expression 55÷11+(18-6)x9 |
Evaluation = 55÷11+(18-6)x9 = 55÷11 + 12x9 = 5 + 12x9 = 5 + 108 = 113 |
Operation Parenthesis Division Multiplication Addition Result |
Example 10 :
Evaluate : (7 + 18) x 3 ÷(2+13) - 28
Expression (7+18)x3÷(2+13)- 28 |
Evaluation = (7+18)x3÷(2+13)-28 = 25x3 ÷ 15 - 28 = 75 ÷ 15 - 28 = 5 - 28 = -23 |
Operation Parentheses Multiplication Division Subtraction Result |
We hope that the students would have understood the stuff given on "Order of operations".
Apart from the example problems explained above, if you want to know more about "Order of operations", please click here.