Alternate Division

I have found that Division can be Alternately done by multiplication. I can explain that with the 'DIVISION BY 9' shortcut. Actually 1/9 = .111111111111111............... . Actually when you multiply a number by 11 you do it same as the steps of Division by 9 except exactly the last two steps. That is what happens here too. If you want to know more you can contact me.

Division by 9

A really awesome trick that simplifies division by 9 to a child's play:

Take a number 333414(Let this be called as the "Q" number). To divide this 333414 by 9:


Steps:
i) Write the first number as it is.
ii)Add this number to the next number in the Q number and this is the next number in the answer. If a two digit number comes up add the tens digit to the previous number in the answer.
iii)Do the same up-to last before digit in the Q Number.
iv)After you add the last number to the final Number i.e "4" (here) you divide the sum by 9 then if any quotient appears add it to the answer and if any remainder appears it is the number that comes as repeating number after Decimal.

If any remainder appears like in 427345, the reminder would be 7. So it would repeat the decimal like .7777777777777 .

So the answer would be: 47482.7777777777777777777777777777777777777777777777777777..........

In my list this is the second most easiest shortcuts ever. Of-course, this is applicable to any number above the Division line. As always, Please practice but especially this shortcut leads very less practice.

                                                                       Thank you.

Information

Please just do not neglect the topics other than the shortcuts. They are all posted for you. So please read them. The posts are, Expanding and condensing pattern, The law of UNIQUENESS, ZERO The expander and like that.

Thank you

Exponential Equations

Equations are the language of nature. When a person is simply forced to mug up an equation he/she tries to mug it up in a detesting mood. But there is no need to mug up. You just have to know why is it so. Exponential Equations are one of the important equations of nature in which its language is so significant. I know that significant word, but exposing in the web leads to criticisms. So just leave it. But to generally look upon the exponential equations, it can be given as:

N = N₀e^±λt

^{Actually here N is the final value. "t" is the time.} 

"λ" is another constant depending on the process.

N_{0 is called as the initial value.}

 _{The main thing here is the "e" called as the exponential constant. It is just a factor that has the value of 2.718. "e" is also called as Euler's constant after the person who gave it i.e. Leonhard Euler.}

_{Now, here what I wanted to tell is the importance of this equation. I will give examples that are of practical life which follow this equation. Population growth attains exponential growth. When you deposit an amount in the bank for Fixed Deposit, after some time that money would have increased in an exponential manner. When you keep a hot cup of coffee to cool down on the table, the speed at which the coffee cools down would be exponential.} 

_{"For this must I know this equation?", if you think like this, just leave that coffee example, but is the fixed deposit example not important to you?}

_{If you had a doubt about} λ, I will tell how it works. The bank will say that that this percent per annum the interest will be calculated no? That percent is that λ. Actually we call the symbol Lambda. If you know about the symbol please do not scold me. Just for others to know.

I think the above content helped you. If you have any doubts about these types of equations or if you have any suggestions also, just mail me at iforindia123@gmail.com. And sorry for the different sizes of text. It may be irritating for some people. Due to addition of symbols and equations into the content such things occurred.Please do not mind it, OK ?!

Thank you

Law of Uniqueness

           Each number whether in a addition or a subtraction or a multiplication or a division process maintains its own individuality.

          In Vedic Division shortcuts what I have observed is that the long form of division is so much reduced in size, that it makes the humans to calculate in a limited workspace. Some may feel that Vedic division is faster. It is because, when one searches for a shortcut, and if this process appears "as" shortcut, they say to themselves, "Oh yes, it is a shortcut. It will help me to do the calculations faster."

          But does it really help to calculate using mind? The real answer is "No". Certain people can do division using Vedic method so quickly because it is due to years of practice. And even some people like Scott Flansburg do the calculations in fractions of second and tell the answer immediately because, it is scientifically observed that, in his brain he has the ability to say the answer by "instinct". The doctor says such abilities may be due to genetic reasons.

         You know, shortcuts must be easier to learn and easier to use. Even the great math Prodigy Shakunthala Devi did not expose her secrets of mental math.

         Let it be. Soon we will find some shortcuts that can be easily practiced and easily used. However division is a different process. But with the help of Law of Uniqueness that numbers retain their individuality in all processes I will try to find some shortcuts in Division.

Thank you 

"Expanding Pattern" and "Condensing Pattern"

Consider like this:

There are only three MAJOR NUMBERS in this world. All the other numbers are their added or multiplied replica.

Say it is like this: 0 and infinity are the two extremities of the positive number line: 1 is the midpoint of this number line. There is infinite distance between 0 and 1(just consider) and there is infinite distance between 1 and infinity. Why i am saying this is you can find infinite number of numbers between 0 and 1 like, 0.1, 0.9, 0.9999, 0.8576, 0.00078544, 0.0506640478 like. Also you can find infinite numbers between numbers 1 and infinity like 2, 3, 6589,787965743559207, and so on.

So you have your calculator with you?

Take a number between 1 and 0, say 0.999 and square it continuously, finally you will only get 0. Of course, there is some negligible number. But when you have squared infinite times it would be a perfect ZERO. Similarly when you take a number between 1 and infinity and square it infinite times you will get INFINITY.

From this it is clear that on squaring a number it takes you to the either extremities of the 01infinity number line. It is like expanding, is it not. So I call powering as "THE EXPANDING PATTERN" when the power lies between 1 and infinity. When you square 1 infinite times you get only 1, because it is the neutral midpoint.

So here, for a simple narration lets take squaring and square rooting.

I call Squaring as the Expanding Pattern.

Now when you take any number between 0 to 1 or 1 to infinity and take root of it with the calculator infinite times you will always get 1. So if the power is fractional on simplifying or if the power lies between 0 to 1, on infinitely taking the root, you get "1" always.

So, regardless whether a number lies close to infinity or close to zero on taking the root continuously or infinite times, you get 1 only. So you are always pulled to the number 1. So I call taking root as THE CONDENSING PATTERN.

Squaring numbers in 50's :

Lets take, 52

Square 52 = 2704

Steps :

1. Add the once digit to 25.
2. Attach the square of once digit. If it is a single digit to fill the vacancy of the tenth digit put zero. Here 04 will be attached to 25+2.
3. So the answer is 2704.

Try all  the numbers in the 50's for practice.