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Distributive property of multiplication

  1. Jul 25, 2012 #1
    OK - this one has been argued to death in several different threads, but the answers have been less than satisfactory... so someone provide a reason why I am wrong here:

    48 / 2(9 + 3) = 2.

    Why? Because the distributive property of multiplication means that 2(9+3) = (2*9+2*3).

    For example, what if we replace (9+3) with x? 48 / 2x = ?

    Yes? No?

    (Apologies in advance for posting yet again that which everyone thinks has been put to rest).
  2. jcsd
  3. Jul 25, 2012 #2


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    That is NOT a matter of the "distributive property", it is just a matter of your notation being ambiguous. That could be interpreted as either
    [tex]48/(2(9+3))= \frac{48}{2(9+ 3)}= \frac{48}{2(12)}= \frac{48}{24}= 2[/tex]
    or as
    [tex](48/2)(9+ 3)= \frac{48}{2}\left(9+ 3\right)= 24(12)= 288[/tex]

    Use parentheses to make your meaning clear.
  4. Jul 25, 2012 #3


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