A while ago, I watched a TV program on how incorporating Indian Mathematics in Japanese schools increased overall achievement in children. Indian Mathematics introduces cool shortcuts in math. The subject really interested me and I started to look into Indian Mathematics methods. Not all of them are easily explained but here are a few that I've learned. Note: This post won't be of interested to those brilliant mathematicians and techies on TechHui who can solve 8 digit problems in their head. Multiplying by 11 What is 26 X 11? It's not rocket science so I'm sure everyone can figure it out but here is how Indian Math solves it. 26 X 11 1. Add 2 + 6 = 8. 2. Put the number between 26. 3. You get 286. 71 X 11 = ? 1. 7 + 1 = 8 2. Put 8 between 7 and 1. 3. 781 Multiplying by Nines (X9, X99, X999....) What is 18 X 99 ? Anytime you are multiplying by 9, 99, 999 e.t.c, you can use this trick. Example: 18 X 99 = ? 1. Subtract 1 from the 18. 18 - 1 = 17. 2. Now subtract 17 from 99. 99 - 17 = 82. 3. Combine 17 and 82. 1782. The answer is 1782. Another example: 208 X 999 = ? 1. 208 - 1 = 207 2. 999 - 207 = 792 Answer: 207,792 This trick only works if the number you are multiplying is less than the nines. So 2562 X 99 would not work with this method. Double Digit Squared If you need to calculate a double digit number by itself (something squared), the Indians figured an easy way to do this. This only works when the last digit is a 5 so 15 X 15, 25 X 25 e.t.c. Here is how to do it. Let's say you need to calculate 25 X 25. 1. Split the number. So with 25, we split it into 2 and 5. 2. Multiply the first number by the number + 1. So in this case it would be 2 X (2+1) = 6. 3. Mulitply the second number by 5. 5 X 5 = 25. 4. Now add put the numbers side by side. 625. The answer is 625. Another example with 35 X 35 that explains it more visually.
As an equation, it would be something like this: a×(a+1)｜b×b
Number Squared as 100 as a base There are also shortcuts to squaring a number using the number 100 as a base. This video explains this pretty well. Double Digit Multiplication What happens if you want to multiply double digits like 47 X 82? How about 78 X 65? Here is how it can be solved. 78 X 65 = ? Multiply the ones digit by ones digit. Then multiply the tens digit by tens digit. In this example, 7 X 6 = 42 and 8 X 5 = 40. So we get 4240.
We now do cross multiplication. We multiply, 8 X 6 and 7 X 5 and place the results after the ones digit. Now you add everything (except the ones digits) and get your answer.
So our final answer is 5070. Here is a video that explains it.
The same method that the Mayan's developed (so I assumed based on the title of the video). They used lines to solve the problem.
Comment by Scott Murphy on April 17, 2009 at 7:44am
Hi Nate,
I hadn't seen those before. I look forward to your article on statistics. Numbers are always fun!
Scott
Comment by Daniel Leuck on April 17, 2009 at 5:11am
Nate Sanders: BTW, nice article and huge props for a math post.
Agreed! I think its our first.
Nate Sanders: I'm working on an article (in my head) right now about something pertaining to statistics that I'll hopefully be able to flesh out enough to write up something here on TechHui.
I look forward to reading this post.
Comment by Nate Sanders on April 15, 2009 at 8:04pm
BTW, nice article and huge props for a math post. I'm working on an article (in my head) right now about something pertaining to statistics that I'll hopefully be able to flesh out enough to write up something here on TechHui.
Comment by Nate Sanders on April 15, 2009 at 7:44pm
"Double Digit Squared" works not only when the ones digit is 5 in both numbers, but whenever the tens digits are the same in both numbers and the sum of the ones digits is 10.
The multiple digit multiplication using only primitive multiplications reminds me of Napier's Bones. I think I first saw these techniques in a book by Shakuntala Devi a long time ago, though, and there are definitely plenty of diagrams in her book for fast multiplication. BTW, I think this is normally called "Vedic Math".
At a higher level, I remember feeling a good bit of awe when I was introduced to Strassen's Method for Matrix Multiplication. He basically figured this out by writing out the dot products involved in a matrix multiplication and factoring out common pieces to cause fewer multiplies and more adds (multiplies were a lot costlier then than they are now).
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