# Rule 23: Order of Operations

The parenthesis instruct you to simplify the expression within the parenthesis before you proceed. The division symbol has the same role as the parenthesis. It instructs you to treat the quantity above the numerator as if it were enclosed in a parenthesis, and to treat the quantity below the numerator as if it were enclosed in yet another parenthesis.

Example: Calculate .

Solution:
The division symbol takes the place of a parenthesis. Therefore, this problem has two parenthesis that must be removed. The numerator must be simplified, and the denominator must be simplified.

The numerator contains multiplication, addition, and subtraction. Complete the multiplication first. can be modified to .

The denominator contains division and addition. Complete the division first. can be modified to .

The problem can now be written .

### If you would like to review more examples, click on the word Example. Work the following problems and click on Answer to check your results.

Problem 1: Calculate .

Problem 2: Calculate .

Problem 3: Calculate .

[Identification] [Factoring Integers] [Reducing Fractions] [Multiplication]
[Order of Operation]

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Author: Nancy Marcus