Years ago a third-grader complained to me that a mean kid at school was calling her "four-eyes". She was bothered and wanted to know how she could put an end to the name-calling. I suggested this reply:
It gives a nice symmetry to the exchange. One person multiplies by two and the other divides. And if the sequences continue, the numbers characterizing the tormentor shrink to nothingness (1, 1/2, 1/4, ...) while those describing the victim (2, 4, 8, ...) grow to infinity and beyond.
By the way, it worked very well at school the next day, and it still makes me smile when I think about it.