Kenneth G. answered • 01/15/14
Tutor
New to Wyzant
Experienced Tutor of Mathematics and Statistics
Hi Toni. Order of operations is not simple. Vivian got the right answer but there is a problem with her explanation. So let me give it a try.
The reason for order of operations is that when you don't use parentheses to separate operations, everybody could get a different answer to the problem. You can see this because Parvis got an answer of 3 which was incorrect.
The PEMDAS acronym is not quite correct because it implies that you do multiplication before division and addition before subtraction in the order and that's incorrect.
In the order of operations, Multiplication and Division are on the same level and Addition and Subtraction are on the same level. If you have operations on the same level, the rule is you work from left to right. Also, for parentheses we work from inner to outer, and we regard an expression in parentheses as a separate problem and use the order of operations rules on what is in the parentheses as a separate problem.
So the original problem is 9*(2+3)/2*4+7.
Steps:
1. Parentheses are first, and inside the parentheses there is only addition, so first we multiply 2+3 = 5
So the problem becomes 9*5/2*4+7
2. Next level is Exponents, but we don't have any exponents
3. Next level is Multiplication and Division. We work left to right
So 9*5 = 45; then 45/2 = 22.5; then 22.5*4 = 90; and the problem becomes 90+7
4. Next level is Addition and Subtraction
So 90+7 = 97. The correct answer is 97.
If we make the order of operations explicit using parentheses, it would be
{ [ [ 9*(2+3) ]/2 ]*4 }+7
(Note that Vivian's parentheses 9*[(2+3)/2]*4+7 are incorrect because she is not working left to right. If she had written [9*(2+3)]/2*4+7 it would have been correct.)
If we want to override the standard order of operations then we could do it using parentheses, like this.
I can re-write the problem as 9 * { ( 2+3) /( [2*4] +7) }.
New problem: 9 * { ( 2+3) /( [2*4] +7) }
Now, because parentheses are the first level, above all the other operations, I first do the inner parentheses 2+3 and 2*4 to get 9*{5/(8 +7)}; then I would add 8+7 because it's in the inner parentheses. For parentheses we work from inner to outer. So I get 9*(5/15) = 9*(1/3) = 3, which is the answer that Parviz got.
Note that you can avoid having to bother with order of operations if you simply add parentheses to clarify what operations you intend to do first. It is good practice to at least include some clarifying parentheses in any problem, but too many parentheses make the problem look messy, so it's a trade-off.
