OK, so the problem is 8/2(2+2).
Everyone agrees that the 2+2 is evaulated first because it is in the parentheses. So the question is the value of
8/2*4
This is an ambiguous expression. But that means we turn to convention. In this case, the *convention* is that multiplication and division are at the same level of precedence and we do the calculation from left to right.
Hence,
8/2*4=(8/2)*4=4*4=16.
Now, it is *possible* to have a convention where multiplication is done before division, which would give
8/2*4=8/(2*4)=8/8=1.
But this is NOT the convention actually adopted in mathematics.
Now, as a mathematician, I would *never* write an expression like this simply because it is ambiguous. I would put in parentheses to make it clear what is intended.
Everyone agrees that the 2+2 is evaulated first because it is in the parentheses. So the question is the value of
8/2*4
This is an ambiguous expression. But that means we turn to convention. In this case, the *convention* is that multiplication and division are at the same level of precedence and we do the calculation from left to right.
Hence,
8/2*4=(8/2)*4=4*4=16.
Now, it is *possible* to have a convention where multiplication is done before division, which would give
8/2*4=8/(2*4)=8/8=1.
But this is NOT the convention actually adopted in mathematics.
Now, as a mathematician, I would *never* write an expression like this simply because it is ambiguous. I would put in parentheses to make it clear what is intended.
