This trick, like several others like it, is easier to remember and work with if one adopts the notation x̅ for ten's complement (10-x), e.g. 4̅ means 10-4=6. S

This trick, like several others like it, is easier to remember and work with if one adopts the notation x̅ for ten's complement (10-x), e.g. 4̅ means 10-4=6. So the trick this post gives is (essentially) that: [x̅] × [y̅] = [x̅+̅y̅][xy] where […] denotes a single digit, as it simply says that (10-x) × (10-y) = 10(10-(x+y)) + xy In this notation, the example given becomes: 6 × 8 = 4̅ × 2̅ = 6̅8 = 48. Note that this also works when there's a carry (write the "carry" digit as a superscript on the left): 6 × 7 = 4̅ × 3̅ = 7̅¹2 = 3¹2 = 42. (I think I first saw this convention with the "vinculum" in Swami Bharatikrishna Tirtha's book Vedic Mathematics which is simultaneously a work of fraud and genius: the book contains several such dazzling tricks that are convenient in special cases, which the Swami must have collected/invented and mapped to a small set of mnemonic rules ("sūtra"s), then (dubiously) described as "Vedic" knowledge as part of an anti-colonialist project. Actually looking at it now, it uses the vinculum slightly differently, e.g. uses 31̅ to mean 29 rather than 39. Another book in that genre is The Trachtenberg Speed System Of Basic Mathematics though it doesn't go as far.)