6^2/2(3)+4=

Question

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

Answer 1

Since most modern calculators follow the order of operations rules, I just entered the problem as written into a calculator and the answer is 10.

Apparently the parentheses on the 3 tells the calculator to multiply 2 times 3 first to get 6. Then 6² /6 is 6 and adding 4 makes 10.

This problem is a matter of interpretation of the math symbols in the written expression, so there will be differences.

Answer 2

P-E-M-D-A-S  (Please Excuse My Dear Aunt Sally) is the rule!  And, if you do (3) first, you will get only 3.

 Ah, now the rub (as Shakespeare would say):

   Is the formula    6^2/(2*3) + 4      (then, why don't they write it correctly?)
              or        (6^2 /2 )* 3 + 4    ?
 

Do (P) first, so the formula is       6^2/ 2 * 3 + 4
Then (E), so                        36 / 2 * 3 + 4
Then (M) or (D), left to right:    18 * 3 + 4
Then (M)                                    54 + 4
Then (A)                                      58
 
Note:  P means do what is inside the parentheses first!

Special note:  Harvey F. and I are having a discussion about whether parentheses constitute implicit multiplication at the high precedence level of parentheses rather that the lower precedence level of multiplication.  Thus, PEMDAS and left-to-right rules are modified.  Any expert knowledge is appreciated (but PLZ don't guess). 


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. Wofram 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.^[7] Newer TI calculators (TI 83 or later) also yield x² in all three cases.
 

[7]   "2x/2x, 2*x/2*x, 2(x)/2(x) - Wolfram|Alpha". Wolframalpha.com. Retrieved 11 February 2013

Answer 3

Your answer depends on how the problem was actually written. There are three possibilities:

 

 

 

1. It's written with a ÷ sign instead of a /, but you substituted a / because you don't have a ÷ sign on your keyboard.

 

In that case, you should evaluate it like you did, getting an answer of 58.

 

 

 

2. It's written as a fraction instead of with a /, where 6² is above the fraction line and 2(3) is below the fraction line.

 

In that case, you should evaluate it like your friends did, getting an answer of 10.

 

That's because fractions introduce hidden parentheses. When using PEMDAS, if you're faced with a fraction like ²⁺³ / ₃₊₇, you should evaluate the expression as though there were parentheses around the top and bottom:

 

(2+3)/(3+7) = 5/10 = 1/2

 

 

 

3. It's written just as you wrote it, with a /.

 

I think this is unlikely, since as you can see, it can be a bit ambiguous written that way. However, if it is written like that, you should evaluate it using PEMDAS as normal, treating the / as division and the () as multiplication. Nothing complicated needs to happen in this case. Multiplication and division written like this happen just like normal multiplication and division:

 

6² ÷ 2 × 3 + 4 = 58

 

 

 

Those methods and answers are the widely-accepted ways of evaluating each of the three expressions, and are almost certainly what your teacher is looking for in each of the three possible cases.

 

Hope this clarifies things!

Answer 4

Harvey F. makes some good points. Another way to see it is when you got 36/2(3) + 4, you should then have followed PEMDAS and done the multiplication next. So that naturally would give 36/6 + 4 = 10. You actually divided first, rather than multiplied.

 

Or, if you consider the parentheses first, then it's 6² /6 + 4 = 10

Maybe parentheses around a single symbol aren't really parentheses....