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==The equation is not ambiguous ==
===6÷2(1+2) is not equal to 6÷2*(1+2)===
Standing alone, 6 will always equal 6 and 2(1+2) will also always equal six6, so dividing these two terms will always equal 1. We would not write 2(a+b) as (2(a+b)), nor would we re-write the given equation as 6÷2*(a+b). Granted, the [https://www.wyzant.com/resources/blogs/14831/the_obelus_for_division obelus (÷)] is an archaic symbol for division, but this is not a postgraduate level equation, this is middle-school level math.
2(1+2) is understood to be a function, placing this function anywhere in a larger equation must always resolve to the same value. The equation, 6÷2(1+2)=? is illustrative to why we cannot substitute explicit multiplication for implied multiplication, in other words, 6÷2(1+2) is not equal to 6÷2*(1+2).