Arithmetic operations involve addition, subtraction, multiplication, division etc. In an arithmetic operation, anything that is not a number may be an operation.
Long ago, there was a lot of confusion in simplifying the arithmetic operations involving more than one operation. Two different students used to get two different answers for a same problem when they take the different priorities for the operations. One student used to addition first and the other student used to do multiplication first.
To avoid this confusion, mathematicians worked a lot and framed some rules which should be followed by one while simplifying an arithmetic expression involving more than one operation.
The rules are as follows:
1) Operate the Parenthesis always first:
Example:
a) 3 x (4+5) = 3 x 9 = 27 (correct)
b) 3 x (4+5) = 12 + 5 = 17 (wrong)
2) Operate Exponents (powers) before multiplication/division:
Example:
a) 3 x 42 = 3 x 16 = 48 (correct)
b) 3 x 42 = 122 = 144 (wrong)
3) Operate Multiplication/Division before addition/subtraction:
Example:
a) 3 + 6 x 5 = 3 + 30 = 33 (correct)
b) 3 + 6 x 5 = 18 + 5 = 23 (wrong)
4) Go always from left to right:
Example:
a) 50 ÷ 2 x 5 = 25 x 5 = 125 (correct)
b) 50 ÷ 2 x 5 = 50 ÷ 10 = 5 (wrong)
These order of operations can be remembered very easily with a phrase PEMDAS, where the alphabets stand for the following operations.
P– Parenthesis
E-Exponent
M-Multiplication
D-Division
A-Addition
S-Subtraction
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