ORDER OF OPERATIONS
How do you calculate 2 + 3 x 7? Is the answer 35 or is the answer 23? To know the correct answer, one must know the correct order of operations with respect to addition, subtraction, multiplication, division, etc.
 Rule 20:
 Multiplication and division must be completed before
addition and subtraction.
2 + 3 x 7 = 2 + 21 = 23 is the correct answer to the above question.
How do you calculate (2 + 3) x (7  3)? Is the answer 32,
20 or is the answer 14? To know the correct answer, one must know the correct order of operations with respect to addition, subtraction, multiplication, division, and with respect to parenthesis.
 Rule 21:
 Expressions in parenthesis are treated as one number
and must be calculated first.
(2 + 3) x (7  3) = 5 x 4 = 20 is the correct answer to the above
problem
How would you calculate [3 + 7  (2 + 3 x 6) +2 x 5 7 +1]?
 Rule 22:
 If parenthesis are enclosed in other parenthesis, work from the inside out.
In the expression, , the expression (2 + 3 x 6) is the inner most parenthesis and must be calculated first. 2 + 3 x 6 = 2 + 18 = 20.
The expression is now modified to . The next parenthesis to be calculated is 7  20 + 2 x 5 = 7  20 + 10 =  13 + 10 =  3.
The expression is now reduced to [3 + {3}  7 + 1] = 0  7 + 1 =  6.
How would you calculate .
 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. When you complete that
task, you have what appears to be two fractions that you are adding.
Not so! can be
written and
multiplication must be completed before addition within each
parenthesis..
= Both
parenthesis have been simplified. Now perform the multiplication to
yield
. The last thing to
do is the addition.
If you would like more examples and problems to work click on the appropriate word.
 Rule 20
 Rule 21
 Rule 22
 Rule 23

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Author: Nancy
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