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<blockquote data-quote="AirElemental" data-source="post: 176466" data-attributes="member: 3742">Ok, so I was a demented little kid.I hated the multiplication tables.I mean, They just seemed redundant to me.I decided I'd figure out a way around em.see, 4x6 seemed an awful lot like 5x5 to me.I quickly learned the connection, and present it to you below:(Note: this method was &quot;Discovered&quot; in elementary school, butI didnt develop the knowledge to explain it till much later.)&nbsp;&nbsp;4x6 = 245x5 = 25.&nbsp; 25-1=24, therefore 5x5-1 = 24 right? follow me?ok now try it with 3x5. should be 4x4-1 right? good. keep going.1x3 =2x2-1.ok so we see a pattern.&nbsp; but what happens when the integersget farther out?&nbsp;1x11.Well, first get the average, or 6 in this case.6x6... now... 6x6 = 36. thats way off of 11.&nbsp; 36-11 = 25. so 6x6-25=1x11?Close.. but.. the way it works is like this:&nbsp;1....6....116-1=5. 11-6=5. hmm.ok so 6x6-5x5=11.1x99=50x50-49x49.or to be&nbsp; more specific,X*Y=((X+Y)/2)^2 - (y-(X+Y)/2)^2.try it. you'll be amazed.then you'll wonder why I went through all the trouble.&nbsp;300 x 400 = 350x350-50x50-1 x -3 = (-2x-2) - (-1x-1)1.5 x 2.5 = 2x2 - .5x.5now that last one makes it much easier to see the answer is 3.75, huh?cheers</blockquote>

[QUOTE="AirElemental, post: 176466, member: 3742"] Ok, so I was a demented little kid. I hated the multiplication tables. I mean, They just seemed redundant to me. I decided I'd figure out a way around em. see, 4x6 seemed an awful lot like 5x5 to me. I quickly learned the connection, and present it to you below: (Note: this method was "Discovered" in elementary school, but I didnt develop the knowledge to explain it till much later.) 4x6 = 24 5x5 = 25. 25-1=24, therefore 5x5-1 = 24 right? follow me? ok now try it with 3x5. should be 4x4-1 right? good. keep going. 1x3 =2x2-1. ok so we see a pattern. but what happens when the integers get farther out? 1x11. Well, first get the average, or 6 in this case. 6x6... now... 6x6 = 36. thats way off of 11. 36-11 = 25. so 6x6-25=1x11? Close.. but.. the way it works is like this: 1....6....11 6-1=5. 11-6=5. hmm. ok so 6x6-5x5=11. 1x99=50x50-49x49. or to be more specific, X*Y=((X+Y)/2)^2 - (y-(X+Y)/2)^2. try it. you'll be amazed. then you'll wonder why I went through all the trouble. 300 x 400 = 350x350-50x50 -1 x -3 = (-2x-2) - (-1x-1) 1.5 x 2.5 = 2x2 - .5x.5 now that last one makes it much easier to see the answer is 3.75, huh? cheers [/QUOTE]

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