The expression 6÷ 2(1+2) is ill-formed if you want to apply PEMDAS. Consider 6/2 × (1+2). This is equally ill-formed for application of PEMDAS. Both symbols, ÷ and ×, have no context. However 6/(2(1+2))=1 has context for application of PEMDAS as does 6/2•(1+2) =9, where the dot, •, is an unambiguous separator between a rational multiplicand and a succeeding expression.

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