Discussion in 'Teacher Time Out' started by Irishdave, Jul 10, 2012.

1. ### AliceaccMultitudinous

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Jul 11, 2012

12/ 2 (1+1) *3

Order of operations stipulates:
Parentheses
Exponents
(multiplication and division) from left to right
(addition and subtraction) from left to right.

So: you do parentheses first: 12/ 2 (1+1) *3
12/2*2*3
Then, since all that's left is mult and division, they go left to right.
6*2*3
The answer is 36.

Sorry, guys, I was in Philly for a few days with mom.

2. ### AliceaccMultitudinous

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Jul 11, 2012

And this, my friends, is exactly how and why I teach Order of Operations.

For what it's worth, the Plurplemath site is the only one I've ever seen that mentions any sort of priority to multiplication symbols. Every other source I've ever seen has said that they're interchangeable.

To quote Algebra Two and Trigometry, by Dressler and Rich: "Evaluate the multilications and divisions in order from left to right." No additional directions about strenght of one symbol over another.

Advanced Algebra with Transformations and Applications by Usiskin, "Third: Multiplication and division, from left to right" with no further instructions about parenthese.

Foundations of Advanced Mathematics, by Ganthert and Brennen, "Then multiply and divide, from left to right." with no additional instructions.
All of these sources are intended for students of Algebra II, where presumably they would handle any exceptions to the rule.

Barrons SAT: "Multiplication and Division: then do all the multiplication and divisions in order from left to right-- do not multiply first and then divide." Nothing else mentioned. And if any ambiguouity did exist, I would imagine ETS would be the first ones to take advantage of it.

Here's a school district site:Oswego, NY schools: http://regentsprep.org/Regents/math/ALGEBRA/AOP2/Lorder.htm

http://www.ehow.com/how_4492937_problems-using-order-of-operations.html "There are exceptions to this rule. Multiplication and Division should be performed in the order that they are written from left to right. That is, if we have the following problems...
20 ÷ 10 x 5, Division is done First and Multiplication Second, so the Solution to this problem is,...20 ÷ 10 = 2. Then 2 x 5 = 10. Similarly, in the problem,
20 x 10 ÷ 5 ,Multiplication is done First and Division second, so the Solution to this problem is,... 20 x 10 = 200. Then, 200 ÷ 5 = 40.
As you read from left to right, if the Operation of Division comes before Multiplication, then Division is done first and Multiplication after. And if the Operation of Multiplication comes first, then Multiplication is done first and Division after."

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Jul 11, 2012

Alice, I understand you. But, it has been along time since I took math. I wonder how one is to know that the 12 is divided only by the 2, and not the whole part of the equation. Would more parentheses help? This is my summer math lesson.

4. ### AliceaccMultitudinous

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Jul 11, 2012

If 12 were to be divided by the rest of the equation, the rest of the equation would have to be grouped together. It could either be all together in the denominator, under the 12, in which case the grouping is implied. Or it could be written like this:
12/ [2 (1+1) *3 ] or 12/ {2 (1+1) *3}

The actual symbol-- parentheses vs brackets vs braces is immaterial.

5. ### jenglish97Devotee

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Jul 11, 2012

Hi Aliceacc ~ Thanks for your input! I want going to write about how 12 can only be divided by the whole thing if and only if it has the parentheses, brackets, or braces. Hopefully people understood how it is only one answer...

Thanks again! Hope you had a nice trip to Philly!

6. ### AliceaccMultitudinous

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Jul 11, 2012

It was delightful, thanks.

7. ### MikeTeachesMathDevotee

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Jul 11, 2012

Thanks!

Microsoft Word 2007 using the built-in equation editor. Then I took a screenshot of it and pasted it into Paint and saved it.

8. ### MikeTeachesMathDevotee

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Jul 11, 2012

Isn't the rest of the expression grouped by multiplication?

9. ### AliceaccMultitudinous

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Jul 11, 2012

Yes. But since you're dividing first, you divide the 12 by the 2, not the 12. If you wanted to divide by 12, those would have to be manually grouped together in one of the 2 methods I mentioned.

10. ### MikeTeachesMathDevotee

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Jul 11, 2012

I still think it's too ambiguous for a definite answer. The question is flawed.

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Jul 11, 2012

I think it is ambiguous by design, perhaps to stimulate exactly the type of discussion we've had about it.

12. ### AliceaccMultitudinous

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Jul 11, 2012

I think the problem is tricky, not ambiguous.

Order of Operations exists to remove the ambiguouity, so that there is only one answer to a problem involving mathematical operations.

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Jul 11, 2012

Thanks Alice. I understand and shall remember should anyone ever need to know.

I constantly surprises me about the things I learn on this site. I learned how to clean my glass stove top with lemon juice and soda on here. I just love to watch it bubble up.

14. ### TeacherGroupieModerator

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Jul 11, 2012

As I noted on page 1,

15. ### AliceaccMultitudinous

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Jul 11, 2012

OK, I stand corrected.

Those are the only two sources I've seen.

16. ### runsw/scissorsPhenom

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Jul 11, 2012

I got 9. If you follow the Please Excuse My Dear Aunt Sally you do the work related to parentheses first (1+1=2, 2*2=4) then multiplication and division left to right (12/4*3=9).

17. ### runsw/scissorsPhenom

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Jul 11, 2012

So what is the correct answer?

18. ### KateLHabitué

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Jul 11, 2012

It's 36. The 2 times 2 is not in parentheses.

19. ### PeachynessVirtuoso

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Jul 11, 2012

Right, if you follow order of operations, the answer is 36.

20. ### Catcherman22Companion

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Jul 13, 2012

Yes.. the only correct answer is 36...

If the original problem wanted us to multiply the 2 times 2 first.. it should have been put into parenthesis or written as described earlier (as a fraction).