Quizzes & Puzzles2 mins ago
6 / 2(1+2) = 7
153 Answers
While the world argues over whether the correct answer is 1 or 9 . . . I get 7 as the answer.
So what's the problem with everyone else?
So what's the problem with everyone else?
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Here, for example, is the expression (as typed) input into the foremost mathematical engine in the world:
https:/
I appreciate that you might read it that way but you have to appreciate that you are mentally inserting something that is not there in order to give you the answer. In fact 6/2(1+2) is equivalent exactly to 6 ÷ 2 * (1+2). I trust that you will see this as (also) 9.
The key thing to remember with every symbol in maths, be it + - x ÷, is that they are binary relations -- they act on the numbers *immediately* on their left and right. Hence the / in the above expression acts only on the 6 and the 2, and doesn't "see" the (1+2).
The picture buenchico links to works out instead the expression 6/(2(1+2)), with the extra brackets. It's clunky to fit into one line, but the key is to try and derive this expression backwards, as follows:
1 = 6/6 = 6/(6) = 6/(2*3) = 6/ (2*(1+2)) = 6/(2(1+2)).
When written in that order, it is clear that the extra pair of brackets was always necessary and cannot therefore be omitted if you want to preserve the same expression. Compare to
9 = 3*3 = 3*(3) = 3*(1+2) = (3)*(1+2) = (6/2)*(1+2) = 6/2*(1+2) = 6/2(1+2)
where in the sixth equality I used that (a) = a and in the final step I simply omitted the multiplication symbol.
I hope this clarifies things. BODMAS is taught badly, and leads to a lot of confusion. I don't think it's anyone's fault, exactly, but the dogma over people who think they are right when demonstrably they are not is troubling, sad, and leads to further innumeracy.
Chris in his latest post is continuing the problem. It's perfectly possible to use / in a single line correctly, and there is no need to mark it wrong (although I agree about the point of clarifying notation -- all I am saying, Chris, is that you apparently don't understand the notation either).
https:/
I appreciate that you might read it that way but you have to appreciate that you are mentally inserting something that is not there in order to give you the answer. In fact 6/2(1+2) is equivalent exactly to 6 ÷ 2 * (1+2). I trust that you will see this as (also) 9.
The key thing to remember with every symbol in maths, be it + - x ÷, is that they are binary relations -- they act on the numbers *immediately* on their left and right. Hence the / in the above expression acts only on the 6 and the 2, and doesn't "see" the (1+2).
The picture buenchico links to works out instead the expression 6/(2(1+2)), with the extra brackets. It's clunky to fit into one line, but the key is to try and derive this expression backwards, as follows:
1 = 6/6 = 6/(6) = 6/(2*3) = 6/ (2*(1+2)) = 6/(2(1+2)).
When written in that order, it is clear that the extra pair of brackets was always necessary and cannot therefore be omitted if you want to preserve the same expression. Compare to
9 = 3*3 = 3*(3) = 3*(1+2) = (3)*(1+2) = (6/2)*(1+2) = 6/2*(1+2) = 6/2(1+2)
where in the sixth equality I used that (a) = a and in the final step I simply omitted the multiplication symbol.
I hope this clarifies things. BODMAS is taught badly, and leads to a lot of confusion. I don't think it's anyone's fault, exactly, but the dogma over people who think they are right when demonstrably they are not is troubling, sad, and leads to further innumeracy.
Chris in his latest post is continuing the problem. It's perfectly possible to use / in a single line correctly, and there is no need to mark it wrong (although I agree about the point of clarifying notation -- all I am saying, Chris, is that you apparently don't understand the notation either).
He may say that, but he is wrong. He is simply wrong. I can't put it any more clearly than that. It does not divide everything on the left by everything on the right. It acts ONLY on the things IMMEDIATELY on its left and right.
Please -- pay attention to the link I gave, where I input the computation *as typed* into Wolfram Alpha. You can also find the same result on Google Chrome, on any other calculator you care to use that allows you to input multiple operations simultaneously. They will all give the answer 9. These are computers, for crying out loud. Once they have been given the rules, they apply them without mistakes and without ego.
You are backing the wrong side. Go and read a maths book, and go and use a maths computer program, and go and educate yourself about basic arithmetic. I am sorry if this comes across as rude but I can't stress enough how angry this makes me.
Please -- pay attention to the link I gave, where I input the computation *as typed* into Wolfram Alpha. You can also find the same result on Google Chrome, on any other calculator you care to use that allows you to input multiple operations simultaneously. They will all give the answer 9. These are computers, for crying out loud. Once they have been given the rules, they apply them without mistakes and without ego.
You are backing the wrong side. Go and read a maths book, and go and use a maths computer program, and go and educate yourself about basic arithmetic. I am sorry if this comes across as rude but I can't stress enough how angry this makes me.
I know I should calm down but I care deeply about maths education and it saddens me when people who think they know what they are doing, but actually don't, continue to hold on to demonstrably false arguments -- especially, in this case, even after it has been demonstrated. And these errors just propagate, because (especially in the case of Chris), some people who don't know what they are doing end up still teaching it (wrongly) anyway. Over something so trivial as this, it is simple enough to check whether or not you are right. And then check again, later. And a third time. And so on.
I hope, Chris, that you absorb what I've said and check again how BODMAS (in particular, the symbol / ) works. You are letting your students down otherwise.
I hope, Chris, that you absorb what I've said and check again how BODMAS (in particular, the symbol / ) works. You are letting your students down otherwise.
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