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What is 48÷2(9+3)?

What is correct answer for 16/2[8-3(4-2)]+1? Some say its 17, some say its 5.

I would definately say it is 5:

16/2[8-3(4-2)]+1
16/2[8-3(2)]+1
16/2[8-6]+1
16/2[2]+1
16/4+1
4+1
5

Even numerous handcalculators and online calculators disagrees about the order of operations.

http://www.wolframalpha.com/input/?i=16%2F2[8-3%284-2%29]%2B1

vs.

http://www.wolframalpha.com/input/?i=16%2F2%288-3%284-2%29%29%2B1

Also why wolframalpha calculates differently when brackets are changed? I am genuinely confused.

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I would agree up to $16/2[2]+1$ this should be $8[2]+1=16+1=17$. Multiplication and division are on the same tier of importance, so reading left the right yields the answer. –  Bill Cook Jan 25 '12 at 14:47
3  
@Srivatsan so there is no correct answer for this. It is just a badly written expression. –  dumbguy1 Jan 25 '12 at 14:53
1  
@Sri, that post was obvious trolling! This post is a duplicate, so... :) –  The Chaz 2.0 Jan 25 '12 at 14:53
2  
Why is this being downvoted? It's a perfectly reasonable question. Moreover, I don't think this is a civil way to treat new users, especially when they take the time to write out their thoughts on the matter. –  David Mitra Jan 25 '12 at 15:07
1  
@David, in light of the comment "so there is no correct answer..." (which indicates that the OP read the linked Q&A), I feel confident that this is a well-intentioned question, and not worthy of a downvote. Closed as Duplicate, sure. –  The Chaz 2.0 Jan 25 '12 at 15:28
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marked as duplicate by Srivatsan, Rahul, Willie Wong Jan 25 '12 at 14:58

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

1 Answer

The ambiguity is whether $x/y(z) = \frac{x}{y}z$ or $\frac{x}{yz}$. Officially, multiplication and division proceed from left to right. Often, however, the precise meaning of the expression is clear enough from context, so people don't really bother with the

Going by the official definition, your simplification of parentheses is correct, but you diverge from accepted order of operations in the fourth-from-last line, when you state $16/2[2]+1 = 16/4+1$. Instead, you should divide and multiply left-to-right: $16/2[2]+1 = 8[2]+1 = 16+1 = 17.$

It doesn't really matter, though. This kind of question is more wordplay than mathematics, sort of like disputes over ending sentences with prepositions or using the Oxford comma: you can cook up examples where imprecise grammar leads to a misunderstanding, but usually everybody understands what you mean.

(Just for fun, consider: "We invited our mothers, JFK, and Stalin" vs "We invited our mothers, JFK and Stalin." This is analogous to $16/2[8-3(4-2)]+1$ vs $16/\{2[8-3(4-2)]\}+1$.)

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