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Order of Operations


Order of Operations

When simplifying an expression that contains several types of operations, it is important evaluate each calculation in a certain order to get the correct end result. This example expression contains parentheses, an exponent, multiplication, division, addition, and subtraction. To simplify the expression, all of these steps must be taken in a particular order.

Order of operations 1.svg

The rules that govern the order in which calculations should be evaluated are known as the order of operations.

Expression Simplified Operation
Parentheses and grouping symbols
Multiplication and Division

There are a few things to note about this simplification:

  1. The addition in the numerator of was evaluated at the same time as the parenthetical expression This is because fraction bars are considered grouping symbols in the order of operations.
  2. Even within grouping symbols, the order of operations must be followed.
  3. The multiplication of and was evaluated in the same step as the division of by This is because multiplication and division are inverse operations, and inverse operations occur in the same "tier" of the order or operations; this rule also applies to addition and subtraction.