Distributive property of multiplication

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SUMMARY

The discussion centers on the interpretation of the expression 48 / 2(9 + 3) and its relation to the distributive property of multiplication. Participants argue that the expression can yield two different results based on the placement of parentheses, leading to confusion. The correct interpretation hinges on clarity in notation, emphasizing that 48 / 2(9 + 3) can be interpreted as either 48/(2(12)) = 2 or (48/2)(12) = 288. The conclusion stresses the importance of using parentheses to avoid ambiguity in mathematical expressions.

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drkent3
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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).
 
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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.
 

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