

Short Methods in Arithmetic - Ixiaus

Someone posted, a while back, a link to the Wired Wiki on some shortcuts in Arithmetic. I thought I would post those plus more that I have found.<p><i>To multiply a number by 5, 50, 500, etc., divide by two and multiply by 10, 100, 1000 (or multiply then divide by two).</i><p>Ex: 84 * 5 = (84 / 2) * 10 = 420<p><i>To multiply a number by 9, multiply by 10 and subtract the multiplier.</i><p>Ex: 35 * 9 = 35 * 10 - 35 = 315<p><i>To multiply by 11, multiply by 10 and add the multiplier.</i><p>Ex: 76 * 11 = 76 * 10 + 76 = 836<p><i>To multiply by 25, 250, etc., divide by 4 then multiply by 100, 1000, etc (or multiply then divide).</i><p>Ex: 52 * 25 = (52 / 4) * 100 = 1300<p><i>To multiply by 125, divide by 8 and multiply by 1000 (or multiply then divide).</i><p>Ex: 848 * 125 = (848 / 8) * 1000 = 106000<p><i>To multiply a number by 33 1/3, 16 2/3, 12 1/2, 8 1/3, 6 1/4, multiply by 100 and divide by 3, 6, 8, 12, or 16 (or divide then multiply).</i><p>Ex: 84 * 8 1/3 = (84 * 100) / 12 = 700<p><i>To multiply a number ending in 1/2, as 2 1/2, 4 1/2, 11 1/2, by itself, multiply the whole number by the whole number plus 1 and add 1/4 to the product.</i><p>Ex: 8 1/2 * 8 1/2 = (8 * (8 + 1)) + 1/4 = 72 1/4 (72.25)<p>Those are all of the ones I've found thus far in my books and on the internet that seem the most applicable (there are some that are shortcuts but they aren't by much).
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RiderOfGiraffes
To square a number, adjust it up and down by the same amount to get two
numbers. If you choose carefully, one of them will be easy to multiply by.
Multiply them, then add the square of the amount adjusted.

Ex: 53 x 53 converts to 50 x 56. 50 x 56 (using your methods) us 100 x 28, or
2800. We adjusted by 3, so add 9 giving 2809.

I used this the other day to compute 3^10 in my head and stunned my work
colleagues.

3^10 = (3^5)^2 = 243^2.

243^2 = 200 x 286 + 43^2 = 57200 + (40x46+9) = 57200 + 1840 + 9 = 59049.

Alternatives:

240^2 + 6x240 + 9 = 57600 + 1440 + 9 which are all numbers geeks might know
(although this is a completely different method)

243^2 = 236 x 250 + 49 = 118 x 500 + 49 = 59 x 1000 + 49

Finally, 3^10 is also 9 x 3^8, and you should all know 3^8 is 6561, because
that's so close to 2^16/10, so the answer is also 65610-6561, but I can't do
subtractions like that in my head.

As with most things, constant practice helps.

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NonEUCitizen
A book I read way back was on the Trachtenberg System. Amazon has it with
ISBN-10: 0313232008 and ISBN-13: 978-0313232008, but way too expensive (I
thought the one I read was paperback). Wikipedia describes it at:

<http://en.wikipedia.org/wiki/Trachtenberg_system>

which also mentions "Vedic mathematics,"

[http://en.wikipedia.org/wiki/Swami_Bharati_Krishna_Tirtha%27...](http://en.wikipedia.org/wiki/Swami_Bharati_Krishna_Tirtha%27s_Vedic_mathematics)

