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Evaluating $$6^2\div 2(3)+4$$

I understand how people are getting $10$ but I am getting $58$ because I am not distributing the $2$ to the $3$ inside the parentheses. Is that correct?

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  • $\begingroup$ What is now the correct answer? I calculated 10. $2(3)$ were closely written together so I assumed it was the denominator of a fraction. $\endgroup$ – Pedro Mar 24 '15 at 2:44
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    $\begingroup$ 58 is right according to order of operations $\endgroup$ – randomgirl Mar 24 '15 at 2:48
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    $\begingroup$ @Pedro Here the parentheses are used to represent multiplication. The expression means $$\frac{6^2}{2} \cdot 3 + 4$$ $\endgroup$ – N. F. Taussig Mar 24 '15 at 3:01
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    $\begingroup$ The correct answer is that it is badly written and ambiguous if there is even a question as to which it means. Write more clearly what you mean: $(6^2/2)\cdot 3+4$ or $6^2/(2\cdot 3)+4$. $\endgroup$ – Jonas Meyer Mar 24 '15 at 3:03
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    $\begingroup$ According to Matlab 6^2/2*(3)+4 gives ans = 58. $\endgroup$ – Pedro Mar 24 '15 at 3:33
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By the Immutable Laws of Emperor Pemdas, you square the 6 first to get 36. Then you divide by 2 to get 18. Then you multiply by 3 to get 54. Then you add 4 to get 58. You are correct. The sticky part is that the 'divide by 2' and 'multiply by 3' operations are at the same ''level'' in the empire of Pemdas so you compute left to right.

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    $\begingroup$ Exactly! Alot of people have the misconception that you have to Multiply first because the 'M' comes first in the PEMDAS. $\endgroup$ – Django Mar 24 '15 at 2:55
  • $\begingroup$ misconception? why do you think D comes before M then- following your logic? $\endgroup$ – sci-guy Mar 24 '15 at 3:09
  • $\begingroup$ Because one has to come first. $\endgroup$ – user223391 Mar 24 '15 at 3:21
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    $\begingroup$ First you calculate what is between the parenthesis. You have $(3)$ which becomes substituted by $3$. From then on, we follow the normal rules. $\endgroup$ – Pedro Mar 24 '15 at 3:26
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This can be written as:

$\frac{6^2}{2(3)} + 4$

$6^2 = 36$

$2(3)=6$

So now we have $\frac{36}{6} +4 = 6+4=10$

OR

$\frac{6^2}{2}(3)+4=\frac{36}{2}(3)+4=18(3)+4=54+4=58$

There is ambiguity in the way it is written - that's why it is so important to be crystal clear when writing math.

I can see you are learning basic arithmetic but down the road you will see far less of the '÷' sign and much more of expressing divisions as ratios (fractions) which removes some of the ambiguity.

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  • $\begingroup$ Yes, a fraction would be less ambiguous but then it would defeat the purpose of testing order of operations I'm guessing. Written exactly how it is if you follow your rules PEMDAS and go from left to right you shouldn't be getting 10 $\endgroup$ – Django Mar 24 '15 at 2:58
  • $\begingroup$ How do you not get 10? the P stand for parentheses - do that first? Then you get 36/6 + 4 = 10 $\endgroup$ – sci-guy Mar 24 '15 at 3:01
  • $\begingroup$ Yes, P does stand for parentheses but its for everything inside the parentheses. Not around it. $\endgroup$ – Django Mar 24 '15 at 3:06
  • $\begingroup$ Fair enough, but M and D can be done in either order - why do you think division before multiplication is correct, and not vice versa? $\endgroup$ – sci-guy Mar 24 '15 at 3:08
  • $\begingroup$ @renegade05 I will upvote your answer tomorrow, I have no upvotes anymore. According to Matlab 6^2/2*(3)+4 gives ans = 58. Anyway, I understand that you find this a stupid question because the way it is stated, it is ambiguous. $\endgroup$ – Pedro Mar 24 '15 at 3:37

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