Kayla R.

# 6^2/2(3)+4=

I followed PEMDAS but I didn't do the parenthesis first because I thought those parenthesis were just to signify multiplication. So I got:
6^2/2(3)+4
36/2(3)+4
18(3)+4
54+4
=58
but other people did 2(3) first and got 10. So what is the answer Stephanie M.

tutor
And, if you're interested in more about the order of operations, here's a useful article:

Also, it should be noted that both 1/2/3 = 0.16666667 and 1/2(3) = 1.5 evaluate using the conventional PEMDAS order. No need to consider parentheses around one number any differently from other multiplication: 1/2/3 = 0.5/3 = 0.16666667 and 1/2(3) = 0.5(3) = 1.5
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07/24/15

## 4 Answers By Expert Tutors

By: David W.

tutor
To Harvey f.:  THX for the experiment (I don't have a calculator since my computers do everything; I also don't need the watch I have;  etc.)

Would you test the calculator's evaluation of the expression
(but, first, decide what you think it should be):    1/2(3)

Technical Note to Harvey F.:  In Programming Languages class, using Data Structures concepts (stack) and Reverse Polish Notation [ which makes precedence specific ], evaluation is easy.  The syntax scanner then has the responsibility to accept/deny the expression -- for example, Excel signals and error for this expression.

Calculator manufacturers have made such errors before.
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07/24/15 David W.

tutor
Note:  I tried Google and Bing; they both say 1/2(3) = 1.5
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07/24/15 David W.

tutor
O.K.   PLZ explain these to me:    =1/2/(3)*4    and   =1/2/(3*4)
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07/24/15 David W.

tutor
I found this on Wikipedia"

1/2x equals 1/(2x), not (1/2)x ... Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics. Wolfram Alpha changed in early 2013 to treat implied multiplication the same as explicit multiplication (formerly, implied multiplication without parentheses was assumed to bind more strongly than explicit multiplication). 2x/2x, 2*x/2*x, and 2(x)/2(x) now all yield x2.   Newer TI calculators (TI 83 or later) also yield x2 in all three cases.

    "2x/2x, 2*x/2*x, 2(x)/2(x) - Wolfram|Alpha". Wolframalpha.com. Retrieved 11 February 2013.
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07/24/15 David W.

tutor
I found this on Wikipedia:

“. . . 1/2x is equal to (1/2)x, and not 1/(2x) .. .”

Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics. Wolfram Alpha changed in early 2013 to treat implied multiplication the same as explicit multiplication (formerly, implied multiplication without parentheses was assumed to bind more strongly than explicit multiplication). 2x/2x, 2*x/2*x, and 2(x)/2(x) now all yield x2. Newer TI calculators (TI 83 or later) also yield x2 in all three cases.

   "2x/2x, 2*x/2*x, 2(x)/2(x) - Wolfram|Alpha". Wolframalpha.com. Retrieved 11 February 2013
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07/24/15 David W.

tutor
I found this on Wikipedia:

“. . . 1/2x is equal to (1/2)x, and not 1/(2x) .. .”

Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.Wolfram Alpha changed in early 2013 to treat implied multiplication the same as explicit multiplication (formerly, implied multiplication without parentheses was assumed to bind more strongly than explicit multiplication). 2x/2x, 2*x/2*x, and 2(x)/2(x) now all yield x2. Newer TI calculators (TI 83 or later) also yield x2 in all three cases.

   "2x/2x, 2*x/2*x, 2(x)/2(x) - Wolfram|Alpha". Wolframalpha.com. Retrieved 11 February 2013
Report

07/24/15 David W.

tutor
I found this on Wikipedia:

“. . . 1/2x is equal to (1/2)x, and not 1/(2x) .. .”

Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.Wolfram Alpha changed in early 2013 to treat implied multiplication the same as explicit multiplication (formerly, implied multiplication without parentheses was assumed to bind more strongly than explicit multiplication). 2x/2x, 2*x/2*x, and 2(x)/2(x) now all yield x2. Newer TI calculators (TI 83 or later) also yield x2 in all three cases.

   "2x/2x, 2*x/2*x, 2(x)/2(x) - Wolfram|Alpha". Wolframalpha.com. Retrieved 11 February 2013
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07/24/15 Harvey F.

tutor
OK David, I am very impressed with your background in calculator programming! My background is less formal. I evaluate 1/2(3) as 1/6 mainly because I was taught that the 1/2 as a factor should be enclosed in parentheses (1/2) to avoid ambiguity. Also the calculator did it this way to get .1666666 repeating or 1/6.
I am thinking this topic needs to be shifted to a forum discussion to involve more tutors without sending all of this to Kayla,the student.
I would suggest a title such as "Fun with PEMDAS".
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07/24/15 David W.

tutor
Frankly, I was quite unaware of a 2013 change.

Both Google and Bing evaluate  1/2/3 as 0.166666  but evaluate   1/2(3)    as 1.5
This means implicit multiplication caused by parentheses takes precedence over left-to-right MD in PEMDAS.

MS Excel and programming languages require '*' and produce an error for 1/2(3)

I'll start a Forum discussion.
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07/24/15

Tutor
4.7 (63)

retired

Kayla R.

Thank you! This makes total sense. It was written with a / not as a fraction. So i had the answer correct. Thank you again!
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07/24/15 Tutor
4.9 (127)

DR ROGER - TUTOR OF MATH, PHYSICS AND CHEMISTRY David W.

tutor
See Wikipedia info below.  Parentheses are now treated as high-level implicit multiplication after the inside contents are evaluated.
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07/24/15 David W.

tutor
Note:  PEMDAS evaluates MD and AS in left-to-right order when parentheses are not present.   1/2/3 is a good example.
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07/24/15

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