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A math problem 6/2(1+2)

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Today, I read the newspaper, and found that there were a lot of people discussing this questions. You can read it from Yahoo! Answer. And there are a lot of people answering this expression equal to 9:

6/2(1+2) = 9

I really don’t understand the possibility of answering it as 9. Some of them said based on PEMDAS, it must be 9; also other said based on distributive property, it is 1.

My answer is 1, and it is impossible to be 9. If using variables for the value inside the parenthesis, then we will get

6/2(a+b)
= 6/(2a + 2b)
= 6/(2(1) + 2(2))
= 6/(2 + 4)
= 6/6
= 1

The above is the distributive property.

This is exactly same as 6/-1(3), which should read as 6/(-1(3)), but not (6/-1)(3).

About Allen Choong

A cognitive science student, a programmer, a philosopher, a Catholic.

3 responses »

  1. Hi Allencch,
    I think that yours calculation isn’t correct. Tipically a “from left to right” operators precedence is used and parentheses are computed first of all, so :

    6/2*(1+2) = 6/2*3 = 3*3 = 9

    It’s the same in C language : http://www.cppreference.com/wiki/language/operator_precedence

    Reply
    • Thanks Angelo. Based on what I read from other resources, especially the newspaper, it mentioned that the question itself produces an ambiguity. That is why, it produces two answer.
      Yes, using C language it produces 9 if using the syntax 6/2*(1+2). Because C language cannot enter the expression as 6/2(1+2).
      I have tried two types of CASIO calculators, which allows to use 6/2(1+2) expression, I don’t know what are the models, one is in white colour, which produces 9; another one is in black colour, produces 1.
      What I written in my post is my answer after the first glance of the question.

      Reply
  2. Ignacio Vázquez Herrera

    The problem when you use the distributive property, is that you distribute the value of 2, instead of 1/2. Check it.

    Reply

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