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How to multiply numbers in your head

Filed in Encyclopedia ,Ideas
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If the numbers are both even or both odd
1. Learn how to square numbers in your head from our earlier post
2. Take the midpoint of the two numbers and square it. For example, if the numbers are 18 and 22, the midpoint is 20, which squared is 400
3. Square the difference between the midpoint and one of the original numbers. For example, the difference between 20 (midpoint number) and 18 (original number) is 2, which squared is 4.
4. Subtract step three from step two. 400 – 4 = 396. Done!

In general, (a + b) * (a -b) = a^2 – b^2. The trick is thinking of the two original numbers as (a+b) and (a-b) which are equally distant from a midpoint a.

If one number is even and the other odd
1. Round one number down or up so that both are even or both are odd. Apply the above method. Do one addition or subtraction to correct for the rounding. For example, think of 18*23 as 18*22 (which we solved above) plus 18.

Grab some pairs of numbers from the grid and try it. You may just like it!

P.S. Andrew Gelman: This is why you’d want to square numbers in your head.

Photo credit: http://www.flickr.com/photos/matthew-h/5579739816


  1. Jay says:

    This is really neat. Are there any similar processes for dividing numbers in your head?

    April 3, 2012 @ 3:47 pm

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