I’m constantly amazed at the number of college students who, through no fault of their own, simply were never taught this simple trick for multiplying by 9 when they were kids.
Why does this trick work? In the picture, if the left pinkie is brought down, there are nine fingers to the right that are up (corresponding to ). If the second finger is lowered and the first is raised, that’s equivalent to adding (since there’s one additional finger in the “tens” part) and subtracting one (since there’s one less finger in the “ones” part). In other words, changing the lowered finger by one digit (pardon the pun) is like successively adding , and successively adding is the same as multiplying by .