Thread: 6÷2(1+2) = ? View Single Post
January 16th, 2013, 07:59 PM   #320 (permalink)
davoid
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Quote:
 Originally Posted by jhawkkw Indeed that is the case. The easiest way to see that by the use of the definition of division of real numbers, and the associative property of multiplication. That definition is a÷b = (a)*(1/b) where (1/b) is a fraction also known as the reciprocal of b. This is the common technique often taught for dividing fractions. (1/2) ÷ (2/3) = (1/2) * (3/2) = (3/4) is an example of this. So applying this property, 6÷2(2+1) = 6*(1/2)(2+1) = 6*.5(2+1). From here, it's much easier to see how one comes up with 9. Using the associative property, which states that you can change the parenthesis order for multiplication only and it doesn't change the outcome, one can come up with (6*.5)(2+1). Going backward across the definition of division, you would get back to (6/2)(2+1).
This I can follow, but the problem is that I see it that where
a÷b = (a)*(1/b), then a=6 and b=2(2+1). This is where the differing solutions diverge, because you see it as a=6 and b=2.

I agree that multiplying by the reciprocal of b is the way to solve the problem...

1 = 0.9999? bring it on!