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 n/n), grouping/parenthesizing/bracketing ((), [] or {})[1] and exponentiation (^ or ⁿ),[2][3] 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
changeFollow all the rules in this order from left to right in the equation.
Brackets and parentheses
changeUse 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
changeWhen 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
changeSolve 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
changeLastly, 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
changeExample one
change- (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 two
change- (7 + 3) * (6 - 3) + 216 / 33
- (7 + 3) * (6 - 3) + 216 / 33
- 10 * (6 - 3) + 216 / 33
- 10 * 3 + 216 / 33
- 10 * 3 + 216 / 27
- 10 * 3 + 216 / 27
- 30 + 216 / 27
- 30 + 8
- 30 + 8
- 38
Acronyms
changeThe acronym for the order of standard operations is GEMDAS/PEMDAS/BOMDAS/BIMDAS, which stands for Grouping/Parenthesization/Bracketing, Exponentation, Multiplication, Division, Addition and Subtraction.[3]
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
changeReferences
change- ↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-22.
- ↑ Weisstein, Eric W. "Precedence". mathworld.wolfram.com. Retrieved 2020-08-22.
- ↑ 3.0 3.1 Stapel, Elizabeth. "The Order of Operations: PEMDAS". Purplemath. Retrieved 2020-08-22.