Indian Mathematics

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.