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 tex2html_wrap_inline25 .

Answer: The answer is 3.

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 tex2html_wrap_inline27 contains multiplication, addition, and subtraction. Complete the multiplication first. tex2html_wrap_inline27 can be modified to tex2html_wrap_inline31 .

The denominator tex2html_wrap_inline33 contains division and addition. Complete the division first. tex2html_wrap_inline33 can be modified to tex2html_wrap_inline37 .

The problem tex2html_wrap_inline25 can now be written tex2html_wrap_inline41 .

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 tex2html_wrap_inline43 .
Answer

Problem 2: Calculate tex2html_wrap_inline45 .
Answer

Problem 3: Calculate tex2html_wrap_inline47 .
Answer

[Identification] [Factoring Integers] [Reducing Fractions] [Multiplication]
[Division] [Building Fractions] [Addition] [Subtraction]
[Order of Operation]

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Author: Nancy Marcus

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