# Distributive property of multiplication

1. Jul 25, 2012

### drkent3

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. Jul 25, 2012

### HallsofIvy

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
$$48/(2(9+3))= \frac{48}{2(9+ 3)}= \frac{48}{2(12)}= \frac{48}{24}= 2$$
or as
$$(48/2)(9+ 3)= \frac{48}{2}\left(9+ 3\right)= 24(12)= 288$$

Use parentheses to make your meaning clear.

3. Jul 25, 2012