How To Show Off Mental Math

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This series started in part 1 with counting, addition, and subtraction, and has slowly built up in complexity. Now we’re doing things at roughly the early algebra level for the last few posts, and we’ll do several more at this level before moving on, to help make sure there’s a good foundation.

I recently re-read the book, Cheaper By the Dozen, by Ernestine Gilbreth Carey and Frank B. Gilbreth Jr. It tells the story of two motion study experts, Drs. Frank Bunker Gilbreth Sr. and Lillian Moller Gilbreth, who brought up a family of twelve in the early twentieth century.

Dr. L.M. Gilbreth found, after her husband’s death, that she could only get consulting work on topics related to the motion study of housewifery. So she applied herself to that, sending all eleven of her surviving children to college. Among other achievements, she invented the foot-pedal trash can lid.

That book mentions that their father taught the children mental arithmetic tricks and gives two examples.

To multiply 44 by 44, first you subtract and see how much greater 44 is than 25. The answer is 19. Then you see how much smaller 44 is than 50. The answer is 6. You square the 6 and get 36. You put the two together: 1936, and that’s your answer. 44 x 44 = 1,936.

To multiply 46 by 46, first you subtract and see how much greater 46 is than 25. The answer is 21. Then you see how much smaller 46 is than 50. The answer is 4. You square the 4 and get 16. You put the two together: 2116, and that’s your answer. 46 x 46 = 2,116.

The reason why this works is very simple, and it’s very easy to adapt. You can use it to quickly square numbers near any reference point, and with a little practice you can do the squares of any numbers you want easily, in your head.

Here’s how and why it works, and how to adapt it for your own use.

Holly’s Substack

How To Show Off Mental Math

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