The Order of operations reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Order of operations

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 powerss, multiplication, and subtraction.

Table of contents

1 The standard order of operations 1.1 Example 2 See also

The standard order of operations

Because of the order Parentheses, Exponentiation, Multiplication/Division, Addition/Subtraction, the mnemonic "Please Excuse My Dear Aunt Sally" is sometimes used as an aid in learning this sequence.

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.

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:

See also

• Common operator notation (for a more formal description)
• associativity
• commutativity
• distributive property

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