## >> Friday, December 25, 2015 Merry Christmas and Happy New Year 2016

## >> Friday, December 18, 2015

What is Digit Sum:
The sum of all the digits in a number is Digit Sum.
e.g. The digit sum of 125 is 1 + 2 + 5 = 8
The digit sum of 1357 is 1 + 3 + 5 + 7 = 16

Some fun with Digit Sums:
Let's add a 2 digit number with the number generated by reversing its digits.
For Example, for 28, we have to add 28 + 82 =  110
Let's see few more examples:
16 + 61 = 77
13 + 31 = 44
38 + 83 = 121
27 + 72 = 99

The result is in a pattern. You can see, all the numbers are divisible by 11.

Let's derive an equation out of the above calculation.

We have a number xy. The number with reversed digits will be yx.

So, xy + yx = 10x + y + 10y + x = 11x + 11y = 11 * (x + y)

So the conclusion is "When we add a 2 digit number with another number resulting from reversing the digits, the result will be 11 times their Digit Sum".

To verify this, let's take above examples again.

28 + 82 =  110 = 11 * (2 + 8)
16 + 61 = 77 = 11 * (1 + 6)

## >> Saturday, August 17, 2013

Today we will learn how to multiply two numbers having first digits same and sum of second digits is 10 using vedic methods.

Let's understand it through examples.

Example 1:  47*43

Here first digits are same, i.e. 4. Sum of second digits is 7 + 3 = 10.
This is exactly the conditions we are talking.

How to find the multiplication result:

Multiply 4 by 4+1, i.e. 4*(4+1)=20
Multiply last two digits, i.e. 7*3 = 21

Now the result is,  47 * 43 = [4*(4+1)][7*3]==2021

Example 2: 52*58

52*58 = [5*(5+1)][2*8] = =3016

Example 3: 84*86

84*86 = [8*(8+1)][4*6] = =7224

Example 4: 75*75

75*75 = [7*(7+1)][5*5] = =5625

Example 5: 69*61

69*61 = [6*(6+1)][9*1] = =4209
Note that in this example, we had to add 0 to make second part a two digit number.

## >> Monday, June 29, 2009

Introduction:
This article will demonstrate how to verify if a numbver is divisible by 7 or not. It will demonstrate using simple vedic ways so that any student, teacher or maths lover can learn it easily.

Testing technique:
1. Double the last digit of the number.
2. Subtract it from the remaining number.
3. Then test the remainder if divisible by 7.
4. If remainder is a large number, repeat steps 1 to 3 again and again till you get a simple number that you can test mentally.

Example:
Let's test 791 to find if it is divisible by 7 or not.
step 1: Lat digit is 1 X 2 = 2
step 2: Remaining number 79 - 2 = 77
step 3: We can say easily that 77 is divisible by 7
Hence, 791 is dividible by 7

Let's test a bit complex number:
7856492

Step 1: 2 X 2 =4
Step 2: 785649 - 4 = 785645 (this is a big number. Repeat step 1 and 2 now)
Step 3: 5 X 2 = 10
Step 4: 78564 - 10 = 78554
Step 5: 4 X 2 = 8
Step 6: 7855 - 8 = 7847
Step 7: 7 X 2 = 14
Step 8: 784 - 14 = 770

Now, easily we can say that 770 is divisible by 7.
Hence the whole complex number 7856492 is divisible by 7.

Hope this helps.

### Test for Divisibility of a number in traditional methods

Introduction:
In traditional methods, we are taught about checking divisibility by numbers like 2, 3, 4, 5, 6, 8, 9, 10 and 11. We will see the divisibility rule for each of the numbers one by one.

Divisibility test by 2:
A number is divisible by 2 if its last digit is divisible by 2.
Means if the last digit of a number is 0, 2, 4, 6, or 8, then it is divisible by 2.

Example: 12, 76, 1546694 are divisible by 2
5, 87, 6865459 are not divisible by 2

Divisibility test by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.

Example: 549: 5 + 4 + 9 = 18 and 18: 1 + 8 = 9. So, 549 is divisible by 3.
124: 1 + 2 + 4 = 7. So, 124 is not divisible by 3.

Divisibility test by 4:
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Example: 124 is divisible by 4 as 24(last two digits of 124) is divisible by 4.
12780 is divisible by 4 as 80 is divisible by 4.
962 is not divisible by 4 as 62 is not divisible by 4.

Divisibility test by 5:
A number is divisible by 5 if its last digit is 0 or 5.

Example: 1265 is divisible by 5
230 is divisible by 5
567 is not divisible by 5

Divisibility test by 6:
A number is divisible by 6 if it is divisible by both 2 and 3.

Example: 432 is divisible by 6 as it is divisible by both 2 and 3.
1439 is not divisible by 6.

Divisibility test by 8:
A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8.

Example: 12108 is divisible by 8
54800 is divisible by 8

Divisibility test by 9:
A number is divisible by 9 if the sum of its digits is divisible by 9.

Example: 549: 5 + 4 + 9 = 18 and 18: 1 + 8 = 9. So, 549 is divisible by 9.
34587: 3 + 4 + 5 + 8 + 7=27 and 27: 2 + 7 = 9. So, 34587 is divisible by 9.
124: 1 + 2 + 4 = 7. So, 124 is not divisible by 9.

Divisibility test by 10:
A number is divisible by 10 if its last digit is 0.

Example: 12650 is divisible by 10

Divisibility test by 11:
Find x = sum of odd numbered digits and y = sum of even numbered digits.
If (x-y) is 0 or multiple of 11, then the number is divisible by 11.

Example:
(1) 121: x = 1 + 1 =2
y = 2
x-y = 0
Hence, 121 is divisible by 11.

(2) 879197: x = 8 + 9 + 9 = 26
y = 7 + 1 + 7 =15
x – y = 26 – 15 = 11
Hence, 879197 is divisible by 11.

I will post content for divisibility test by prime numbers like 7, 13, 17, 23 etc which are not taught in our school sylabus.

Regards,
Banshi.

### Vedic Mathematics - Finding Square of a number made easy

Find Square Of a number with Simple and faster Vedic Ways:
Vedic mathematic contains a lot of formulae (Sutra) that not only allows us to do calculations without pen and paper, it also makes our brain to act faster. Now-a-days, to crack in a competitive exam, we must look into two factors, they are SPEED and ACCURACY. By learning Vedic mathematics, one can achieve these two important factors to crack in any competitive exam.

This document contains formulae for finding out square of a number accurately without pen and paper. The formulae are easy to understand and are demonstrated in easy manner with examples.

### 1. Find Square of a number ending with 5:

1.1 Example: Let’s find out square of 25. a. Break the number to two parts with 2 as first part and 5 as second part
b. Find multiplication of 2 and (2+1), i.e 2 x 3 = 6
c. Find square of 5, i.e. 25
d. Hence, our answer, 25² = 6 25=625
1.2 Lets take another example, i.e. 65 a. 65 = 6 5
b. 6 x (6+1) = 42
c. Square of 5 = 25
d. Hence, 65² = 42 25 = 4225

1.3 Let’s take a 3 digit number, i.e. 125
a. 125 = 12 5
b. 12 x (12 + 1) = 156
c. Square of 5 = 25
d. Hence, 125² = 156 25 = 15625
This way this rule can be used to calculate square of numbers ending with 5 without help of pen and paper.

### 2. Find Square of a number which is adjacent to a number that ends with 0 or 5:

We can easily find out square of a number that ends with 0 or 5, e.g. 10, 15, 20, 25, 30 etc.
Now we will see how to find out square of an adjacent number like 11, 9, 16, 14, 21, 19 etc
2.1 Example: Let’s find out square of 31.
a. We know square of 30, i.e. 30² = 900
b. Now, 31² = 30² + (30 + 31) = 900 + 61 = 961

2.2 Lets find out square of 46
a. 45² = 2025
b. 46² = 45² + (45 + 46) = 2025 + 91 = 2116

2.3 Lets find out square of 71
a. 70² =4900
b. 71² = 70² + (70 + 71) = 4900 + 141 = 5041
Now, let’s find out numbers which are 1 less to numbers ending with 5 or 0
2.4 Find square of 14
a. 15² = 225
b. 14² = 15² – (14 + 15) =225 – 29 = 196
2.5 Find square of 29
a. 30² = 900
b. 29² = 30² – (29 + 30) = 900 – 59 = 841

### 3. Find out Square of a number near 100:

Let’s find out square numbers which are close to 100 and are lesser than 100.
3.1 Find square of 97
a. 97 is 3 less than 100 (i.e. -3)
b. 97² = 97 -3 / 03² = 94 / 09 = 9409 (There should be two digits (09 instead of 9) after ‘/’)
3.2 Find square of 96
a. 96 is 4 less than 100 (i.e. -4)
b. 96² = 96 -4 / 04² = 92 / 16 = 9216
3.3 Find square of 87
a. 87 is 13 less than 100 (i.e. -13)
b. 87² = 87 -13 / 13² = 74 / 169 =7569 (There should be two digits(69 out of 169), hence 1 is carry forwarded from 169 and added to 4 of 74)

Let’s find out square of numbers which are close to 100 and are greater than 100.
3.4 Find square of 103
a. 103 is 3 greater than 100 (i.e. +3)
b. 103² = 103 +3 / 03² = 106/09 = 10609
3.5 Find square of 107
a. 107 is 7 greater than 100 (i.e. +7)
b. 107² = 107 +7 / 07² = 114 / 49 = 11449
3.6 Find square of 113
a. 113 is 13 greater than 100 (i.e. +13)
b. 113² = 113 +13 / 13² = 126 / 169 = 12769 (1 is carry forwarded from 169)

I hope this material was helpful to you. I will add some more materials on Addition, Multiplication, Subtraction and Division and other formulae related to Algebra once I compile them.

## >> Wednesday, May 13, 2009

Hello Friends,

This blog is created to share all Vedic maths techniques with you. Using the Vedic maths techniques, you can solve difficult mathematical problems easily and all in mind without pen and paper. You will learn maths in the fun way.

This blog will illustrate all Vedic Maths techniques in simple and easy to understand manner with sufficient examples.

It is targetted to all age group those who have passion to learn. Especially Children, Parents, School and College Students, Job Aspirants and Teachers can take maximum benefit from this site.

Now a days, in each and every competitive exam, competition is very tough. To crack in a competitive exam, two factors are most important, they are Speed and Accuracy. Vedic maths will help you to achieve those two.

If you have any relevant issues or problems, post your queries here. I guarantee that you will get a prompt response.

Regards,
Banshi.

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