how to multiply easily
Here follows a short tutorial with simple calculations: 1. When calculating one bind numbers like in 8,9=89. 2. When adding and subtracting one go from left to right 16+17= (1+1) , (6+7) = 2,(13) =(2+1),3 =33. [ These steps are carried out mentally. Then with a simple subtraction we get 27-19= (2-1) ,(7-9) = 1,(-2) = 10-2=8 or mix (2-1),7 - 9 =17-9 =[ use all from 9 and the last from 10] = 7+1 =8. 3. the rule to check an addition or subtraction is the following, let the a, b be numbers that lie in Z+ , and S be an operator that sum the digits in the number representation. Then the rule
S(S(a)+S(b))=S(a+b) can be used to check if it is correct. Example 27 +19 = 46 : check S(S(27) +S(19))=S(9+10)=S(19)=S(10)=1=S(46)=S(10)=1 , OK!. This also works with a multiplication : a*b=c with the check S(S(a)*S(b))=S(c) . 4. Square numbers with 5 : 75^2 = 7*(7+1), 25 = 5625 . 5. The multiplication method used in the thread with examples from cmd. This provides a fast way to expand your mental multiplication table with numbers like 14*17= (14+7), 4*7 = 21,28 = 238 and with squares that are easiest to remember mentally. There are a lot more methods but those have more conditions. Google Vedic mathematics to learn more. These methods are very useful with large numbers, but one can practice the ideas on small problems to get better faster. The source that I've used is an introduction by Kenneth Williams called 'The art of mental math ' or something similar. It covers the most basic methods, but I will eventually order 'the real deal' , I mean the books with the complete theory. ]
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