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I'm wondering what is the fastest way to multiply numbers? For now, let's focus on 2-digit numbers and were one cannot use scrap paper.

I've come across 3 fast methods:

64x43

1)

    60x43 + 4x43         (note that 60x43 is actually a 1-dig. times 2-dig problem)
    2580  + 172  = 2752

2)

      64x43 = 60x40 + 4x3   =2412
             + 4x40  +3x60  = 340        
                            =2752

3)

             64
            x43
           =-----
            (4x3)   (4 from 64)          12
      (6x3)+(4x4)   (cross multiply)    34
    (6x4)                              24   
                                    ------------+
                                       2752     

*I am aware to some multiplications can be done faster with specific tricks, for example if we square a number, if one of the numbers ends with 5 or is equal to 11, or if they both end in the same number, or if one is close to a multiple of 10, or if one is a product of two 1 digit numbers, etc. But my question regards the general case.

Now practice makes perfect, but before I start training one method I would like to know which one is to be preferred. Is there someone who can say something useful about this? I guess method 3 is not ideal, since the speed of doing the cross multiplication is partly because of the way it is denoted in this example (one above the other). So can someone say whether method 1 or 2 is to be preferred in sense of speed/simplicity?

Related: What is the fastest way to multiply two digit numbers?

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What I usually do, which is probably not the fastest way, is try to look for patterns that I can resolve easily and split the numbers accordingly.

For example, in your case, $$64\times43 = 64\times32+64\times11$$ I immediately recognize $64=2^6$ and $32=2^5$, and I know how to quickly multiply by $11$, so I get $$64\cdot43 = 2^{11}+640+64=2048+704 = 2752$$

While strictly speaking this is not the "general case", I find that every time I have to multiply two digit numbers, a trick like this is possible - and I find it to be the most fun way to do it. This is probably hard to scale to more than two digits though.

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  • $\begingroup$ Nice indeed. But not what I am looking for since 2^11... yeah not so much. I do know a trick for 11, while we're on it: ABx11=A[A+B]B, and if A+B>9 carry the 1. So 35x11=3[8]5 (since 3+5=8) and 92x11 = 112= 9[11]2 = 1012 $\endgroup$ – Cindy88 Feb 28 '14 at 12:13
  • $\begingroup$ Well then you can try: $43=44-1=4\cdot11-1$. Therefore $64\cdot43=64\cdot(4\cdot11-1)=704\cdot4-64=2816-64=2752$ - just work with whatever tricks you can compute quickly and split the numbers. Learning the first powers of $2$ is recommended either way, though. $\endgroup$ – Alfonso Fernandez Feb 28 '14 at 17:09
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may be my article will help you. Here I have described how one can calculate multiplication of two digit numbers mentally. http://mathsequation.com/how-to-memorize-multiplication-table-fast/

64*43= 64*40 +64*3 so basically problem breaks into multiplication of two digit number with 1 dgit like 64*4, 64*3 which can be done mentally easily ,I have explained that too. also once you calculate 64*40=2560 and 64*3=192 mentally. you can add them by my mental addition trick written here.

http://mathsequation.com/mental-addition-trick-learn-within-5-minutes/

I have also explained some additional methods in special cases we can use.

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