ORDER OF OPERATIONS: Example 4

Rule 23:
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 4: Calculate y tex2html_wrap_inline38 and reduce.

Answer: The answer is 2.

Solution:
The division symbols of each fraction takes the place of parentheses. Therefore, before you can add the fractions, you must reduce them. Before you can reduce them, you have to simplify the numerators and the denominators.

Simplify the left fraction first by simplifying its numerator and denominator. The numerator is simplified with the following steps:

tex2html_wrap_inline40

Simplify the denominator of the left fraction next. tex2html_wrap_inline42

The left fraction tex2html_wrap_inline44

Now follow the same procedure for the right fraction. The numerator tex2html_wrap_inline46 .

The denominator tex2html_wrap_inline48

The right fraction tex2html_wrap_inline50 .

The problem tex2html_wrap_inline38 can now be written tex2html_wrap_inline54 .

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