Limitations of Vedic Math Part 1

Vedic mathematics principles have limitations. The applicability has to be further tested before actual use of the principle and the bounds of its applicability. However in squaring two digit numbers ending with 5. the principle can be used. For example consider a number n 5, where n can take values between 0 and 9 and including them, then

 n5 x n5 = n(n+10)25

Because 10 = 1 mod 9, this becomes

n5 x n5 = n(n+1)25

Put any value for n, between 0 and 9. This will work.

If n = 7, 75² = (7 x 8)25 = 5625

Tip #8: Solving Simultaneous Equations Part 1

Solving Simultaneous Equations Part 1:

To solve a set of simultaneous equations, order the equations as if you were solving them by elimination. Then, the numerator of the variable you are solving for is the coefficient of the other variable in the first equation times the constant in the 2nd equation minus the coefficient of the other variable in the 2nd equation times the constant in the first equation. The denominator of the variable you are solving for is the coefficient of the variable you are solving for in the 2nd equation times the coefficient of the other variable in the first equation minus the coefficient of the variable you are solving for in the first equation times the coefficient of the other variable in the 2nd equation. An example is shown in the video.

 

Tip 7: Find the 10s complement of a number

This will begin to be more useful as I put up more advanced tips and such.

To find the 10s complement of a number, subtract each of the digits except the rightmost digit of this number from 9. Subtract the rightmost digit from 10. These digits, from left to right, form the 10s complement. An example is in the video above.

Tip #6: Convert Kilometers to Miles

This is by no means going to be exact, but it will give you a rough idea of how many miles is in a given number of kilometers and vice versa.

To convert from kilometers to miles, simply divide the number of kilometers by 8 and then multiply by 5.

To convert from miles to kilometers, do the reverse: Divide by 5, then multiply by 8.

Here’s a couple of examples:

1. 80 kilometers = 80/8 * 5 miles = 10 * 5 miles = 50 miles
2. 80 miles = 80 /5 * 8 kilometers= 16 * 8 kilometers = 128 kilometers.

 

Feel free to comment on any of these posts or send me an email at vedicmathforkids@gmail.com if you have any questions.

Introduction to the History of Vedic Mathematics

“The world owes most to India in the realm of mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity. The success of Indian mathematics was mainly due to the fact that Indians had a clear conception of the abstract number as distinct from the numerical quantity of objects or spatial extension.”
A.L. Basham, Australian Indologist in The Wonder That Was India

Vedic mathematics has a misnomer. The name makes one think that this comes from one of the 4 Vedas, Rigveda, Yajurveda, Samaveda, and Atharvaveda.  These are the 4 true Vedas. But sometimes other ancient texts from the Vedic Age are mistakenly labeled as Vedas, a notable example being Ayurveda, which isn’t actually one of the Vedas. Rather, it is an ancient form of medicine, analogous to Vedic mathematics.

Vedic mathematics were first written thousand of years ago in the Ganita Sutras, texts that were, until the early 20th century, lost to time due to lack of translation. People ignored them because they couldn’t find any traditional mathematics in them. But it was the work of one man that started a whole cascade of events that popularized Vedic mathematics: Bharati Krishna Tirthaji.

A Sanskrit expert and expert mathematician, Bharati Krishna Tirthaji delved into the Ganita Sutras. After much translation and interpretation, he found that there was math to be had in the Ganita Sutras. It was just bad wording (just like SAT questions) that confused many. As such, he translated these confusing phrases into sutras in modern terms and in a way that people could understand.  This is how Vedic mathematics started. Until next time…

Tip #5: Square any two-digit number

To square any two digit number, follow these three simple steps:

1. Take each digit and square it. Then concatenate the two numbers. If  one of the squares is less than 10, use 0 as a placeholder.
2. Take the two digits and multiply them. Then multiply by 2. Add a 0 on to the end.
3. Add your answers from steps 1 and 2.

I’ll demonstrate with an example:

Say you want to find 56².

1. Start by taking the two digits and squaring them. 5² is 25, and 6² is 36. Concatenate them to get 2536.
2. Take the two digits and multiply them. 5 x 6 = 30.
3. Multiply this by 2. 30 x 2 = 60.
4. Add a zero on to the end to get 600.
5. Add the two numbers you got in the previous steps. 2536 + 600 = 3136.

And there you have it! 56² = 3136!

A Tip for Older People: Differential Calculus

Say an equation is factored as y = (x+a)(x+b)(x+c) and so forth.

Then dy/dx = the sum of the various factor products, taken n-1 at a time.

This means that if the factored polynomial has n factors, each factor product has n-1 factors.

Example #1:
   y = x2 + 3x + 2 = (x+1)(x+2)
Then     dy/dx = (x+1) + (x+2)
Example #2:
   y = x4 + 10×3 + 35×2 + 50x + 24 = (x+1)(x+2)(x+3)(x+4) … factor the polynomial, if possible

   dy/dx = (x+2)(x+3)(x+4) + (x+1)(x+3)(x+4) + (x+1)(x+2)(x+4) + (x+1)(x+2)(x+3)
     
   d2y/dx2 = 2{(x+3)(x+4) +(x+2)(x+4) + (x+2)(x+3) + (x+1)(x+4) + (x+1)(x+3) + (x+1)(x+2)}

   d3y/dx3 = 6{(x+1) + (x+2) + (x+3) + (x+4)2}

Easily Add And Subtract Fractions

Tip #3:

Today’s Tutorial is how to easily add and subtract fractions.

First multiply the numerator of fraction 1 with the denominator of fraction 2. This is the first part of the new denominator. Then comes the operation. The second number in the new numerator is the numerator of the 2^nd fraction multiplied by the denominator of the first fraction. The denominator of the new fraction is just the product of the denominators. If you have more than 2 fractions, just do this in groups of 2. Perform the operation in the numerator, then reduce.

Btw, I’ll also be posting a practice worksheet that you can do. Check the answers on your calculators after you have done them. If you have any questions, email me at vedicmathforkids@gmail.com.

Tip #2 – Multiply numbers quick and easy

Today’s tip is an elegant way of multiplying numbers  using a simple pattern.

For example 21×23=483

So how do you  get this?

We first write 23 below 21. We multiply vertically, that is,first we multiply 2 by 2 to get 4. We do the same for the other end, and multiply 1 by 3 to get 3. The middle is a bit complicated. We do two cross products and add them. In this case, we add the product of 2 by 3 to the product of 2 times 1. This is the middle digit. If the middle is greater than 10, 1 is added to the left.

Another example is 33 x 44.

First do it the Vedic way, and get an answer. Then do it the traditional way. The answer is in the video.

I’ll also be posting a practice worksheet that you can do. Check the answers on your calculators after you have done them. If you have any questions, email me at vedicmathforkids@gmail.com.

Tip#1: Find the square of any number ending with 5.

Today’s tutorial involves finding the square of ANY number ending in “5”.

For example, 75² = 5625.

So how do you  getthis? (By the way, if you came here ready with a calculator, throw it out the window, because as far as Vedic math is concerned, a calculator = cheating! If you came with pencil and paper, keep it for the first few, and then throw them out the window too. These tips are supposed to make math easy, so easy that you can do it mentally and not break a sweat!)

Alright, since the last digit is 5, the answer always includes 25. If you haven’t noticed this, the square of 15 is 225. It has a 25 in it. The square of 25 is 625. It too has a 25 in it.

So write down 25 in your nice little blank. Now comes the first part.

Take the rest of the number that doesn’t include the 5 you handled with the 25 a few moments ago. Find the number one more than it. In other words, add 1 to it. Now take this new number and multiply it by the old number (the number you added 1 to to get the new number). In other words, you are squaring a number, then adding the number to the result. Try it with the square of 75.