To me, "divide A into B" sounds like a some sort of anachronism that you might find in a 17th century one-room schoolhouse, while "divide B by A" sounds perfect

To me, "divide A into B" sounds like a some sort of anachronism that you might find in a 17th century one-room schoolhouse, while "divide B by A" sounds perfectly natural. I went to school on the US East Coast, so you might be onto something here.