Welsh mathematician Robert Recorde’s 1543 textbook Arithmetic: or, The Ground of Arts contains a nifty algorithm for multiplying two digits, a and b, each of which is in the range 5 to 9. First find (10 – a) × (10 – b), and then add to it 10 times the last digit of a + b. For example, 6 × 8 is (4 × 2) + (10 × 4) = 48.

This works because (10 – a)(10 – b) + 10(a + b) = 100 + ab, and it saves the student from having to learn the scary outer reaches of the multiplication table — they only have to know how to multiply digits up to 5.

(From Stanford’s Vaughan Pratt, in Ed Barbeau’s column “Fallacies, Flaws, and Flimflam,” College Mathematics Journal 38:1 [January 2007], 43-46.)