Order of operations and variables - XP Math - Forums

 XP Math - Forums Order of operations and variables

 09-14-2011 #1 tcondon Last Achievements   Join Date: Sep 2011 Posts: 2 Order of operations and variables best strategy to explain how to solve the following problem: 12^2 / 4b + 4 when b=9 Some students evaluated teh problem and got 8 while others got 338.
 09-15-2011 #2 Mr. Hui Last Achievements     Join Date: Mar 2005 Posts: 10,650 Corrected. Thank you jcsites and MAS1. ${12^2}\div4*b+4$ Substitute the value of 9 for b: ${12^2}\div4*9+4$ Evaluate exponents: $144\div4*9+4$ Divide: $36*9+4$ Multiply: $324+4$ Add: $328$ __________________ Do Math and you can do Anything! Last edited by Mr. Hui; 09-24-2011 at 09:46 PM..
 09-21-2011 #3 Jonathan W Guest   Posts: n/a 328 Pemdas 12 ^ 2 / 4 * 9 + 4 144 / 4 * 9 + 4 36 * 9 + 4 324 + 4 328 Last edited by Jonathan W; 12-31-2011 at 07:32 PM.. Reason: Huge Mistake
09-22-2011   #4
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Quote:
 Originally Posted by tcondon best strategy to explain how to solve the following problem: 12^2 / 4b + 4 when b=9 Some students evaluated teh problem and got 8 while others got 338.
It should be 328. The precedence of operation is as follows: exponentiation, division, multiplication and addition. Some got 8 because they first multiplied 4 with 9. However, since division and multiplication are of the same precedence, division is evaluated first.

 09-23-2011 #5 tcondon Last Achievements   Join Date: Sep 2011 Posts: 2 Rules that apply? Edit: Please check the correction in post #2 That is the rule that states you do 4b before dividing 144/4? Anything about solving teh variable expressions first. Even the responses on this question are not the same. I appreciate any feedback. Last edited by Mr. Hui; 09-24-2011 at 09:43 PM..
 09-24-2011 #6 Mr. Hui Last Achievements     Join Date: Mar 2005 Posts: 10,650 Edit: Please check the correction in post #2 __________________ Do Math and you can do Anything! Last edited by Mr. Hui; 09-24-2011 at 09:43 PM..
09-24-2011   #7
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Quote:
 Originally Posted by Mr. Hui You can do 144/4 or 4b first. The order does not change the answer.
I think this a case where a pair of parentheses can clear up a lot of confusion.

Mr. Hui is assuming that the above expression, as written, is equivalent to:

12^2 / (4b) + 4 so that when b = 9 the answer is 4. When he says it doesn't matter what order you evaluate 144/4 or 4b first he is assuming you would get either 144/4/9, or 144/36 which are the same.

However, others are assuming that the expression is equivalent to:

(12^2 / 4) x b + 4 which evaluates to 328.

As the expression is originally written I believe it has to be evaluated the second way so that the answer is 328.

12^2 / 4b + 4
144 / 4b + 4 Evaluate exponents
36 x b + 4 Evaluate division left to right
36 x 9 + 4 Substitution
324 + 4 Multiplication

The 4b term is what is confusing as we are used to treating it as a term in itself so that it seems like we have 144 / 36 when b = 9.

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