6÷2 = 6×½.
6÷2(1+2) = 6×½(1+2).
The ambiguity is caused by people who prioritize implied multiplication over stated multiplication. So they are using PEiMDAS/BOiDMAS, not PEDMAS/BODMAS.
Under PEMDAS/BODMAS, implied multiplication is the same as multiplication, so:
6÷2(1+2) = 6÷2×(1+2) = 6×½(1+2), and the result of that is always 9.
6÷2 = 6×½.
6÷2(1+2) = 6×½(1+2).
The ambiguity is caused by people who prioritize implied multiplication over stated multiplication. So they are using PEiMDAS/BOiDMAS, not PEDMAS/BODMAS.
Under PEMDAS/BODMAS, implied multiplication is the same as multiplication, so:
6÷2(1+2) = 6÷2×(1+2) = 6×½(1+2), and the result of that is always 9.