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In arithmetic and elementary algebra, certain rules are used for the order in which the operations in algebraic expressions are to be evaluated. These precedence rules (which are mere notational conventions, not mathematical facts) are also used in many programming languages and by most modern calculators. In computing the standard algebraic notation is known as infix notation. This article assumes the reader is familiar with addition, division, exponential powers, multiplication, and subtraction.

1 The standard order of operations

1. Evaluate subexpressions contained within parentheses, starting with the innermost expressions. (Brackets [ ] are used here to indicate what is evaluated next.)

2. Evaluate exponential powers; for iterated powers, start from the right:

3. Evaluate multiplications and divisions, starting from the left:

4. Evaluate additions and subtractions, starting from the left:

The expression: 2 + 3 × 4 is evaluated to 14, and not 20, because multiplication precedes addition. If the intention is to perform the addition first, parentheses must be used: (2 + 3) × 4 = 20.

In the UK, the acronym BODMAS is used for Brackets, raise to the power Of, Division, Multiplication, Addition, Subtraction. The "O" may also stand for "or", or may by replaced with an "I", for Indices.

In the USThe United States of America also referred to as the United States U. America ¹ or the States is a federal republic in central North America, stretching from the Atlantic in the east to the Pacific Ocean in the west. It shares land borders with Canada in, the acronym PEMDAS (for Parentheses, Exponentation, Multiplication/Division, Addition/Subtraction) is used instead, sometimes expressed as the mnemonicA mnemonic ( SAMPA /n@'mAnIk/ in US or /n@'mQnIk/ in UK) is a memory aid. Mnemonics are often verbal, are sometimes in verse form, and are often used to remember lists. Mnemonics rely not only on repetition to remember facts, but also on creating associat "Please Excuse My Dear Aunt Sally".

1.1 Example

• Given:

• Evaluate the innermost subexpression (7 + 1):

• Evaluate the subexpression within the remaining parentheses (5 − 8):

• Evaluate the power of (−3)²:

• Evaluate the multiplication 9 × (−5):

• Evaluate the subtraction 3 − (−45):

• Evaluate the addition 48 + 2:

2 See also

• Common operator notationIn computing, common operator notation is just one way of notating mathematical expressions as a linear sequence of tokens, or operators, but this is not the only way. The use of operator precedence classes and associativities is just one way. However, it (for a more formal description)
• associativityAbstract algebra Algebra In mathematics, associativity is a property that a binary operation can have. It means that the order of evaluation is immaterial if the operation appears more than once in an expression. Put another way, no parentheses are requir
• commutativity
• distributivityIn mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra. For example: : 4 · (2 + 3) (4 · 2) + (4 · 3) In the left-hand side of the above equatio