A Classic

(i) Old Way

According to the old way, it should be

Answer
= 6 /[2*(1 + 2)]
= 6/[2*3]
= 6/6
= 1

If you key in exactly as given in the image into an ‘old’ calculator model, you would get this answer.

(ii) New Way

According to the ‘new’ way popularised more by the American Mathematicians (I think) through even the programming of the Google calculator or other type of online calculators as well,

Answer
= [6/2]*(1 + 2)
= 3*3
= 9

Conclusion

Why are there two different ways?

Simply because the “BODMAS” or PEMDAS Rules do “not” cover this particular ‘way of writing’ sufficiently and thus may be “interpreted” in the two different ways as described above (both endorsed by top Mathematicians).

Now, this is not a problem with Mathematics but rather a “notational or way of writing” problem which did not ‘sufficiently cover the meaning of this particular mathematical sentence type’.