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Short Methods in Arithmetic
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.
To multiply a number by 5, 50, 500, etc., divide by two and multiply by 10, 100, 1000 (or multiply then divide by two).
Ex: 84 * 5 = (84 / 2) * 10 = 420
To multiply a number by 9, multiply by 10 and subtract the multiplier.
Ex: 35 * 9 = 35 * 10 - 35 = 315
To multiply by 11, multiply by 10 and add the multiplier.
Ex: 76 * 11 = 76 * 10 + 76 = 836
To multiply by 25, 250, etc., divide by 4 then multiply by 100, 1000, etc (or multiply then divide).
Ex: 52 * 25 = (52 / 4) * 100 = 1300
To multiply by 125, divide by 8 and multiply by 1000 (or multiply then divide).
Ex: 848 * 125 = (848 / 8) * 1000 = 106000
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).
Ex: 84 * 8 1/3 = (84 * 100) / 12 = 700
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.
Ex: 8 1/2 * 8 1/2 = (8 * (8 + 1)) + 1/4 = 72 1/4 (72.25)
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).
- RiderOfGiraffes 17y agoTo 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.
- NonEUCitizen 17y agoA 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 http://en.wikipedia.org/wiki/Trachtenberg_system which also mentions "Vedic mathematics," http://en.wikipedia.org/wiki/Swami_Bharati_Krishna_Tirtha%27s_Vedic_mathematics http://en.wikipedia.org/wiki/Swami_Bharati_Krishna_Tirtha%27...