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 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:

Simplify the denominator of the left fraction next.

The left fraction

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

The denominator

The right fraction .

The problem can now be written .

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