6÷2(1+2) is a simple, well formed, unambiguous problem of division, a÷b, where a=6 and b= 2(1+2), which simplifies to 6. 6÷6=1
Question of notation: axb=ab, and/or any other character, for example c. If we want to show the factors of c, we write (axb).
Factor out the a from (axb) and we get a(b). Thus, ab=c=(axb)=a(b).
a(b) is not interchangeable with a x b, because a(b) represents a product, (a SINGLE number) while a x b is an expression, that is, TWO numbers connected by an operator. However, if we enclose axb in (), it becomes interchangeable with a(b).
Illustration: If 6÷6=1, and 6=2x3, does 6÷6 = 6÷2x3 or 6÷(2x3)????
Easy Rule: Whenever switching from Implicit to Explicit multiplication, ALWAYS enclose the factors involved in ().
Finally, remember that different calculators work differently. Read the instructions, and adjust input accordingly. We should be able to get the same answer on any and all calculators, every time, all the time. If we don't, the problem is probably with our input, not the calculator.