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You want to add 9+3, and multiply that by 2, and then divide 48 by that product. You will get 2. How do you express what you just did?
48÷2(9+3) is the only way.
You get 288 is by dividing 48 by 2, and then multiplying that by the sum of 9 and 3. How do you express that?
(48÷2)(9+3) = 288. Not the same.
The correct answer is 2. Now I remember why I loved algebra. It taught me to think, which turned out in later life to be very useful.
It boils down to weak syntax and using an inferred operator. Those who take the inferred operator as having to hold to the left to right processing order will get one answer, those who tend to group before doing a left to right order will get the other. It doesn't happen as much in math as in everyday language. I always get a kick out of the signs and advertising that tout "Big Baby Sale." If you don't buy in to the convention that there is an unsaid word, you go looking for babies to buy.
Although the 288 version is technically correct, it is sloppy.
It's wrong because after you do the parentheses (9+3), you work left to right. The expression would be better if you added the parentheses, but in algebra they are not necessary.
48÷2(9+3)
48÷2(12)
24(12)
288
If you want 2 the correct expression would be
48÷(2(9+3))
When expressions have more than one operation, we have to follow rules for the order of operations:
First do all operations that lie inside parentheses.
Next, do any work with exponents or radicals.
Working from left to right, do all multiplication and division.
Finally, working from left to right, do all addition and subtraction.
You want to add 9+3, and multiply that by 2, and then divide 48 by that product. You will get 2. How do you express what you just did?
48÷2(9+3) is the only way.
You get 288 is by dividing 48 by 2, and then multiplying that by the sum of 9 and 3. How do you express that?
(48÷2)(9+3) = 288. Not the same.
The correct answer is 2. Now I remember why I loved algebra. It taught me to think, which turned out in later life to be very useful.
Wow. You just lost all credibility on this board.
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