ORDER OF OPERATIONS: Example 1

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 1: 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, division, and addition. Complete the multiplication and division first working with the numbers on either side of the signs in a left-to-right manner. can be modified to .

The denominator contains multiplication, division, addition, and subtraction. Complete the multiplication and division first working with the numbers on either side of the signs in a left-to-right manner. can be modified to .

The problem can now be written .