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Math: 6÷2(1+2) = ?
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[quote:fnord 32102656:MV8xNDczMDcwXzM1NjQ1MTA0X0ExNkYyODY2] [quote:Anonymous Coward 32057798:MV8xNDczMDcwXzM1NjQ0ODk4X0NFNzY4M0VF] Look at any book. All fractions used as coefficients use [u]6[/u]n 2 or (6/2)n therefore, to distribute 6/2, you would NEED parentheses around it. Otherwise, you distribute the 2 into the parentheses, which is called "Eliminating parentheses by distribution". It is not performing multiplication operator, since it is a "property" of math, ie, equality, and you are REPLACING, not multiplying. This is where other people are confused. They think "distributive property" is bound to the order of operations as part of multiplication. It is not. So, What do we have? 2(2+1) is 2 quantities, or groups, of 2+1. In English, "I have 2 bags, with 2 apples and 1 orange in each bag." ie, 6 pieces of fruit. Therefore 2(2+1) = [(2+1) + (2+1)] 6 ÷ [(2+1) + (2+1)] = 1 Ans: 1 Back to 6 ÷ 2n = 3/n. n = 2+1. Ans: 1 again. Distribute: 6 ÷ 2(2+1) = 6 ÷ [2(2) + 2(1)] 6 ÷ 6 = 1 If I add the 2+1 first, i STILL have to distribute, using the Identity Law of a+0 = a 6 ÷ 2(2+1) = 6 ÷ 2(3) = Here, I still have parentheses with a coefficient, so I can still distribute like this: 6 ÷ 2(3 + 0) Here I used the identity law to make it clear 6 ÷ [2(3) + 2(0)] 6 ÷ 6 = 1 No matter what math laws, rules, axioms, or properties are used, you always get ONE if you apply the rules correctly, which is the great thing about math, there is only [b]ONE [/b]correct answer for simple equations like this one. [/quote] The answer depends not only upon the relative precedence of multiplication/division, parenthesation, and addition/subtraction, but also on whether a left to right rule is in force in the evaluation of operations of the same precedence. For instance, if one assumes that operations of the same precedence are evaluated left to right, and parenthesized expressions are evaluated first, the evaluation proceeds as: 6/2(2+1)=3*(2+1)=3*3=9 If operations of the same precedence are evaluated right to left, and parenthesized expressions are evaluated first, the evaluation proceeds as: 6/2*(2+1) = 6/2*3 = 6/6 = 1 [/quote]
Original Message
Alright, there's a lot of self-proclaimed experts around these parts. Let's see how your logic holds up against some basic mathematics.
6÷2(1+2) = ?
I'll give two hints. This is
NOT
a trick question, and there is only
1
correct answer.
All tools used for computation are fair game.
(Yes, I saw this somewhere else and decided to post it here.)
Best of luck to all you geniuses .
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