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Alternate Division Algorythm


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9 replies to this topic

#1 BMAD

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Posted 20 July 2013 - 06:03 AM

Prove (verify) or disprove the following algorithm for division
 
 
The algorithm is quite simple.
 
1. Write the two numbers (each 2 digits in length) that you are multiplying side by side.
 
2. Create a column under the number on the right. Each entry should be half of the entry above it, ignoring any fractional amounts (example: if the number 5 is the right column, the number below it should be 2), stopping when the number 1 appears.
 
3. Create a column under the number on the left. Each entry should be twice the entry above it. Stop when the left column has the same number of entries as the right column.
 
4. Cross out any number in the left column whose corresponding number in the right column is even.
 
5. Add the numbers in the left column which are not crossed out.
 
The number you find in step 5 is the product of the two numbers you started with!
 
Example:
 
 32  25
 64  12
128   6
256   3
512   1
-------
800
So 32 x 25 = 800.

Edited by BMAD, 20 July 2013 - 06:04 AM.

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#2 DeGe

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Posted 21 July 2013 - 12:11 PM

Spoiler for I think

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#3 BMAD

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Posted 21 July 2013 - 05:54 PM

Try an odd case and see if you are correct.
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#4 BMAD

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Posted 21 July 2013 - 07:29 PM

Just realized that I meant multiplication in the title, lol...oops
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#5 Barcallica

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Posted 22 July 2013 - 05:23 AM

Spoiler for I think

That is not true. 

Spoiler for


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#6 BMAD

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Posted 22 July 2013 - 05:36 AM

Excellent...continue
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#7 Barcallica

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Posted 22 July 2013 - 07:32 AM

Spoiler for Continueing


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#8 BMAD

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Posted 22 July 2013 - 07:46 AM

Spoiler for Continueing

this is one approach

Spoiler for but

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#9 Barcallica

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Posted 22 July 2013 - 07:57 AM

 

Spoiler for Continueing

this is one approach

Spoiler for but

 

Interesting, I have no idea how you could connect it to geometry.


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#10 BMAD

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Posted 22 July 2013 - 01:26 PM

Spoiler for specific example to start an outline for a more general proof

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