Date: 07/23/2002 at 18:11:25 From: Emily Wong Subject: Two-digit multiplication Hi, My name is Emily and I was wondering how I could learn to do harder multiplication by heart. I always have to do it on a piece of paper. I can solve them, but it takes more time. 99x99 98x99 15x15 25x25 35x35 45x45 etc. Do you have any tips? Emily
Date: 07/24/2002 at 13:33:00 From: Doctor Ian Subject: Re: Two-digit multiplication Hi Emily, If you _really_ want to do them 'by heart', you'll just have to memorize them. That seems like a lot of work, though. For two-digit multiplications like these, I'll usually use the distributive property. For example, 15 * 17 = 15 * (10 + 7) = 15 * 10 + 15 * 7 = 150 + (10 + 5) * 7 = 150 + 70 + 35 = 150 + 105 = 255 That still seems like a lot of work, doesn't it? Well, note that 17 = 10 + 7 = 20 - 3 so 15 * 17 = 15 * (20 - 3) = 15*20 - 15*3 = 300 - 45 = 255 I can do the same thing with something like 98 * 99 = 98 * (100 - 1) = 98*100 - 98*1 = 9800 - 98 = 9702 The general idea is to use the distributive property to allow you to quickly get close to the answer, and then add or subtract a small number to get the exact answer. It still takes some practice to get good at this, but a lot less than it would take to memorize all the possible two-digit multiplications! Does this help? The BEATCALC (Beat the Calculator) archive on the Math Forum site has some tricks for multiplying by 15, 25, 99, etc. You might enjoy browsing starting at: Multiplying a 2-digit number by 99 http://mathforum.org/k12/mathtips/multiplyby99.html - Doctors Ian and Sarah, The Math Forum http://mathforum.org/dr.math/
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