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, tex2html_wrap_inline68, 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 totex2html_wrap_inline70 . 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 tex2html_wrap_inline74 .

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! tex2html_wrap_inline74 can be written tex2html_wrap_inline78 and multiplication must be completed before addition within each parenthesis..

tex2html_wrap_inline80 = Both parenthesis have been simplified. Now perform the multiplication to yield tex2html_wrap_inline82 . The last thing to do is the addition. tex2html_wrap_inline84

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 Marcus

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