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Early Times

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) x (10 - b), and then add to it 10 times the last digit of a + b.
For example, 6 x 8 is (4 x 2) + (10 x 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.)

June 28, 2022June 27, 2022 | Science & Math

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