Order of operations

The order of operations is a mathematical and algebraic set of rules. It is used to evaluate (solve) and simplify expressions and equations. The order of operations is the order that different mathematical operations are done. The standard mathematical operations are addition (+), subtraction (−), multiplication (*, ×, · or n), division (/, ÷, : or ), grouping/parenthesizing/bracketing ((), [] or {}) and exponentiation (^ or ⁿ), which includes root extraction (√).

Mathematicians have agreed on a correct order to use operations, and it is very important that they know these rules. When people are solving a problem with more than one operation, they will need to know the correct order to solve the problem correctly. Otherwise, the answer will be wrong.

 Rules 
Follow all the rules in this order from left to right in the equation.

 Brackets and parentheses 
Use operations inside brackets and solve any indices. You should always solve brackets first when solving an equation.

Example:
2 * 4 + (9 - 8) + 3
2 * 4 + (9 - 8) + 3
2 * 4 + 1 + 3
2 * 4 + 1 + 3
8 + 1 + 3
8 + 1 + 3
9 + 3
9 + 3
12

 Exponents 
When seeing an exponent, solve it first after solving the brackets. (53 = 5 * 5 * 5 = 125)

Example:
53 * 7 + 4
53 * 7 + 4
125 * 7 + 4
125 * 7 + 4
875 + 4
875 + 4
879

 Multiplication and division 
Solve any multiplication and division in the problem. Note that multiplication does not precede division; this is a common mistake. Both are solved from left to right as they occur.

Example:
5 * 4 - 9 / 3
5 * 4 - 9 / 3
20 - 9 / 3
20 - 9 / 3
20 - 3
20 - 3
17

 Addition and subtraction 
Lastly, solve any addition or subtraction. It always goes from left to right.

Example:
10 - 9 + 4
10 - 9 + 4
1 + 4
1 + 4
5

 Examples of all rules 
 Example one 
(1 + 8) * (4 - 1) + 16 / 23
(1 + 8) * (4 - 1) + 16 / 23
9 * (4 - 1) + 16 / 23
9 * 3 + 16 / 23
9 * 3 + 16 / 8
9 * 3 + 16 / 8
27 + 16 / 8
27 + 2
27 + 2
29

 Example one 

34 * 3 + 4^2 =
34 * 3 + 4^2 =
34 * 3 + 16 =
34 * 3 + 16 =
102 + 16 =
102 + 16 =
118

 Acronyms 
The acronym for the order of standard operations is GEMDAS/PEMDAS/BOMDAS/BIMDAS, which stands for Grouping/Parenthesization/Bracketing, Exponentation, Multiplication, Division, Addition and Subtraction.

When solving 8 - 7 + 5, some people say that 7 + 5 must take precedence, but this is incorrect. Instead, one should look from left to right to find the correct answer. This rule also applies to multiplication and division.

 Related pages 

 Associativity
 Commutativity

 References 

Category:Arithmetics