6/2*(1+2) is 1 or 9?

Question

Possible Duplicate:
What is 48÷2(9+3)?

Please, look at the picture?

Which calculator shows true result and how to prove achieved result?

Answer 1

The reason why calculators are giving different results is because one is calculating,

$$\frac{6}{2\cdot(2+1)} = 1$$

while the other is calculating,

$$\frac{6}{2}\cdot(2+1) = 9$$

Depending on what you want to calculate, you could obtain different answers.

Answer 2

Despite every personal belief, a notation like $a/b(c+d)$ is ambiguous. At school I learned that this should be $$ \frac{a}{b}(c+d), $$ but even in research papers somebody could read $$ \frac{a}{b(c+d)}. $$

Answer 3

when two operations have same precedence, then the operations are done from left to right.So here, division is done first and then multiplication.This is just a convention.Without this, this expression is ambiguous.