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{{ printedBook.courseTrack.name }} {{ printedBook.name }} 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. $(1+2)⋅3_{2}−25+5 =? $ 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.

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

Expression | Simplified | Operation |
---|---|---|

$(1+2)⋅3_{2}−25+5 $ | $3⋅3_{2}−210 $ | Parentheses and grouping symbols |

$3⋅3_{2}−210 $ | $3⋅9−210 $ | Exponents |

$3⋅9−210 $ | $27−5$ | Multiplication and Division |

$27−5$ | $22$ | Subtraction |

There are a few things to note about this simplification:

- The addition in the numerator of $25+5 $ was evaluated at the same time as the parenthetical expression $(1+2).$ This is because fraction bars are considered grouping symbols in the order of operations.
- Even within grouping symbols, the order of operations must be followed.
- The multiplication of $3$ and $9$ was evaluated in the same step as the division of $10$ by $2.$ 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.