Easy Vedic Maths ™

Sutra - All from 9 and the last from 10 (Explained)

2010-07-21T01:19:00.000+05:30

This is an explanation to one of the 16 sutras of Vedic Mathematics. This sutra is popularly known as "All from 9 and the last from 10 ". This sutra (Original name- Nikhilam Navatashcaramam Dashatah) is helpful in making subtraction easy.

NOTE: This sutra is useful in cases of subtraction where a number is subtracted from a number being 10ⁿ (example- 10, 100, 1000 and so on..)

RULE: All the digits of the number should be subtracted from 9 and the digit in the last place should be subtracted from 10. (Easy, isn't it?)

Starting with an easy example first:
Subtracting 1 0 0 - 5 3

So, the answer becomes 47 . This was a example where the number we subtract is of same number of digit as the number of zeros in the number we subtract from (In our case, 100 has 2 zeros, and 53 is of 2 digit).

Now, what if the number of zeros is more than figures of the number being subtracted. Taking the same example as above,
Lets subtract 1 0 0 0 - 5 3 .
In this case we simply suppose 5 3 as 0 5 3 :

So, the answer becomes 9 4 7.

Let's take one more example to make things more clear.
Now we'll subtract 1 0 0 0 - 2 6 7 (We see that no. of zeros and the figure in the number we subtract are same, similar to the first example)

So, the answer becomes 7 3 3.

Now, You must have found it very easy to understand. Why don't you try to solve some of them yourself?

Self-Exercises :-

a) 1 0 0 - 2 8 =
b) 1 0 0 - 7 6 =
c) 1 0 0 0 - 4 6 3 =
d) 1 0 0 0 - 6 3 =
e) 1 0 0 0 0 - 4 6 3 1 =

Answers: a) 7 2 (b) 2 4 (c) 5 3 7 (d) 9 3 7 (e) 5 3 6 9.

Easy Multiplication of numbers around 100

2009-03-29T20:25:00.000+05:30

Multiplication of two numbers around 100 is even easier than you could ever imagine.

Suppose you want to multiply any two numbers, lets take 95 and 97 for example.

Step 1: We'll find out the difference of the two numbers (95 & 97) from 100.

95 is 5 less than 100 [100-95=5],

97 is 3 less than 100 [100-97=3].

Step 2: Subtract the total difference from 100. Here the total difference will be 8 [Since 5 + 3 = 8]

So after subtracting , we get 92 [ 100 - 8 = 92 ]. This becomes first part of our answer.

Step 3: We multiply the two difference amount i.e. 5 & 3 to get 15 as the second part of our answer.

So our final answer becomes 9215. Easy isn't it ?

If you still didn't get it , here's another example for you.

Suppose you mulitiply 88 & 96.

Step 1: Difference of the two numbers ( 88 & 96 ) from 100 are 12 and 4 respectively.

Step 2: Subtracting the total difference of 16 [100- (12 + 40)] from 100 we get 84. [100 - 16 = 84]. So 84 becomes the first part of our answer.

Step 3: Now, we multiply the two difference amount of 12 & 4 to get 48 as second part of our final answer.

So the final answer becomes 8448 .

Self-Exercises:-

a) 92 x 93 =

b) 94 x 98 =

c) 88 x 85 =

d) 87 x 99 =

Answers: a) 8556 (b) 9212 (c) 7480 (d) 8613 .

You might also like: Easy way to multiply with 5 ..

Mental Calculation of Subsequent number 's Square

2009-03-19T23:09:00.000+05:30

It is practically easy to calculate the square of the subsequent number if you know the square of the number.
For example, if you know the square of 10, You can figure out the square of 11 mentally and instantaneously.
Here is how you can do it.
Continuing the above example, Square of 10 is 100, So, square of 11 will be 121.
How ???

First, we multiply 10 with 2 to get 20 and add 1 to it to get 21. [We used: 2A + 1 ( Where A is 10 here)]
Next, we add 21 to 100 (Because 100 is the square of 10)

Similarly, if we want to calculate 51², then
We, Know 50²=2500;
So, 51²= 2500 + (2 x 50) + 1
= 2500 + 100 + 1
= 2601 (Easy, isn't it ?? )

Theory behind it-
(a + b)²= a² + 2ab + b²

If we know a², and b is 1 , then , formula becomes

(a + 1)²= a² + 2a + 1

So, its very easy to solve such square in your head alone. You can do it mentally with a little practice.

Self Exercises:-

a) 61²=
b) 13²=
c) 71²=

Note: This method can also be used for numbers which are not subsequent, this can be dont by placing any other number in place of "b" in the formula.

Easy Multiplication of a number with 5

2009-03-18T17:22:00.000+05:30

It may be difficult for you to multiply a number with 5 , specialy larger numbers like "34638445" , "43574683", or even more larger than this. But after you learn this technique, you can even multiply larger numbers than the above mentioned numbers.
Here is how you should go:
Suppose, You want to multiply 264 with 5, then..

write or imagine mentally:

[ Note: We have replaced the value of "5" with "10/2" ]

=>2640 / 2= 1320 [ You can mentally divide any number with 2, just move from lefthandside first number to righthandside last number, in this example, we should take "2" as the first number , as "2640" is what we have to divide with 2, so start dividing the numbers mentally, start putting the final answer in our mind, like in this example, start dividing "2" ,"6","4" and "0" with 2, and write or imagine the final answer as 1320. ]

If you still didn't get this principle, for You I am putting more examples for you to cover any aspect that is possible.

More Examples :-

563254 x 5 = 563254 x ( 10/2 ) = 5632540 / 2 = 2816270 (final answer)
You can do this mentally in one step once you master the practise.
In this example, you can directly imagine a zero in the end of the number which you want to multiply 5 with ( This is because, when you multiply any number with 10, the number remains the same and gets an additional zero at the end of the number, for example 1265 x 10 = 12650 , 2485x 10 = 24850 and "M" x 10 = M10 , where M can be any digit or number ), and then you can divide it by 2 in your head mentally or even write at a paper , whichever you feel comfortable with.
The process is the same for multiplying any bigger numbers with 5.
Self-Exercises :-
a) 48662 x 5 = ?
b) 1548994 x 5 = ?
c) 3397551 x 5 = ?

If You still have any doubt, be free to leave a comment here with your name and email id, I'll contact You soon.

You might also like this post: Easy way to multiply numbers around 100 and Easy Numbers' Multiplication with 11 ..

Easy Multiplication with 9 ( The Finger Rule)

2009-03-16T21:06:00.003+05:30

This method is applicable for multiplying 9 with numbers upto 10 .
This method requires the use of your hands, this method is very easy to learn.
This method covers a very limited amount of numbers (i.e numbers ranging between 0 - 10 ) But You'll definately find it very interesting and easy..

Here is how to do it-

Firstly, Spread your hands in front of you.
Now suppose you want to multiply 4 with 9, then fold down the 4th finger from your left.

Now notice that there are 3 fingers on the left of your folded finger, and 6 fingers from the right of your folded finger. So the answer becomes 36.
Apply the same method for multiplying any other number between 0 to 10 .
If you still didn't understood.. Don't worry, we have a video explanation too for you ..

Self-exercises:-

a) 9 x 5 =
b) 9 x 7 =
c) 9 x 9 =
d) 9 x 4 =

If you liked it leave your comment below...

Easy Addition of Three-Digit Numbers

2009-03-16T14:57:00.000+05:30

While adding Three-Digit Numbers, we'll use the same method for which we used for Two-Digit addition and Basic addition .

For addition of 355, 752 and 694 together you would say in your head, "three fifty-five, add seven hundred, (ten fifty-five), add fifty, (eleven hundred and five), plus two, (eleven oh seven), plus seven hundred less six, eighteen hundred and one". Or, you may prefer for the addition from left to right; adding the hundreds first, then the tens and then the units.

With a little practise, you will find such addition problems very Easy .

[Mental addition is more easy than the effort of finding a pen and paper or retrieving a calculator from your bag. ]

Carryout some more addition in the exercises below, you'll surely find them easy now!

Self-Exercises:-

a) 359 + 523 =
b) 123 + 458 =
c) 456 + 298 =
d) 345 + 288=

Answers- a) 882 (b) 581 (c) 754 (d) 633 .

Most Easy Trick for learning Table of 9

2009-03-15T13:52:00.000+05:30

This is not related to vedic mathematics, this is just an easy trick for the 9 times table up to 9x10. First, write the numbers

0-9 down the left hand side:

0
1
2
3
4
5
6
7
8
9

Then, repeat the process of writing the numbers 0-9, this time going
UP the right side:

09
18
27
36
45
54
63
72
81
90

Now you have your 9's times table:

9 x 1 = 09
9 x 2 = 18
9 x 3 = 27
9 x 4 = 36
9 x 5 = 45
9 x 6 = 54
9 x 7 = 63
9 x 8 = 72
9 x 9 = 81
9 x 10 = 90

Have fun!
Easy....... isn't it?

Two-Digit Easy Mental Addition

2009-03-08T20:07:00.000+05:30

How would you add 48 ? To add 48, You would add 50 and subtract 2.

How would you add 67 ? To add 67 ,You would add 70 and subtract 3.
How would you add 96 ? To add 96, You would add 100 and subtract 4.
There is a simple principle for mental addition ( With this Easy Vedic Maths principle You can learn to add two digit numbers very easily.. Just remember the principle ..) -

If the units digit is high, round off to the next ten and then subtract the difference. If the units digit is low, add the tens, then the units.

With a little practise, you will be amazed at how you can keep the numbers in your head.
Why don't you try this yourself...

Self-exercises:-

a) 34 + 48 =
b) 75 + 32=
c) 26 + 49=
d) 56 + 45=
e) 82 + 59=
f) 74 + 26=
g) 54 + 67=

Also check out Easy numbers Addition (Basics) & Easy Three-Digit Numbers Addition ..

Easy numbers Addition (Basics)

2009-03-08T19:30:00.000+05:30

Generally for peoples making addition is easier than subtraction. We will learn how to make addition even more easier.
>How would you add 68 plus 9 in your head?
The easy way would be to add 10 to 68, (78), and take away one (1). The answer will be 77.
It is easy to add 10 to any number mentally; 27 plus 10 is 37; 249 plus 10 is 259, etc. Simply increase the tens digit by 1 each time you add 10 to a number.
Here is a basic rule for adding mentally :

To add 9, add 10 and subtract 1; to add 8, add 10 and subtract 2; to add 7, add 10 and subtract 3, and so on.

If you wanted to add 36 , you would add 40 and subtract 4 . To add 295, add 300 and subtract 5. This makes it easy to calculate mentally. To add 67 to a nubmer, add 70 and subtract 3 . To add 385 to a number, add 300 and subtract 15.

Now try these quickly in your head. Call out the answers. For 57 + 9 , don't call out, "sixty-seven, sixty-six". Make the adjustments in your head while you call out the answer. Just say, "sixty-six". Try the following examples ( don't worry, Hints are given to help you out in case you need assistance )

a) 89 + 8 = ? [Hint: Add 10 to 89 and subtract 2 from it. Step 1 > 10 + 89 = 99 , Step 2> 99 - 2 = 97 (Your final answer) .]
b) 75 + 9 = ? [Hint: Add 10 to 75 and subtract 1 from it. Step 1> 75 + 10 = 85, Step 2> 85 - 1 = 84 (Your final answer).]
c) 54 + 7 = ? [Hint: Add 10 to 54 and subtract 3 from it. Step 1> 54 + 10 = 64, Step 2> 64 - 3 = 61 (Your final answer).]
Self-exercises :-
a) 76 + 9 = ?
b) 153 + 8 = ?
c) 278 + 6 = ?
d) 95 + 8 = ?

Also check out Easy Three-Digit numbers addition ..

Squaring of a number ending with 5

2009-02-18T19:38:00.000+05:30

After you read this article , you would be able to find the answers to the square of numbers ending with 5, almost instantly and mentally.
For example , you squares of 35 , 75 , 95 , 105 etc.
Here's how to do it,

Imagine in mind the number, suppose 35 in your mind to be of two parts "3" and "5" ( If it is difficult for you to imagine , write it at a piece of paper )
Now, multiply the first part of the number with a number that is one ( 1 ) greater than it ( Here, "3" is to be multiplied with "4" as 3 + 1 = 4 ) , this will be the first part of your final answer.
Here, 3 x 4 = 12 , so , 12 will be the first part of your final answer.
Next we know 5²=25 , so 25 will be the next part of your final answer.

SO, your final answer becomes 1225 .
Likewise,
95²= ( 9 x 10 becomes the first part, and 25 becomes the next part )
= ( 90 , 25 ) [In the above step "9" is multiplied with "10" since 9 + 1 = 10 ]
= 9025 [ Final answer ]

Taking another example,

105²= ( 10 x 11 becomes the first part, and 25 becomes the next part )
[ Note : The first part will always be the number(s) except 5 ]
So,
105²=( 110 becomes the first part, and 25 becomes the next part )
= 11025 [Final answer ]

Self-Exercies:-

a) 55²= ??
b) 65²= ??
c) 125²= ??
d) 205²= ??

Multiplication with 11

2009-02-18T18:54:00.001+05:30

Multiplication with 11 looks difficult, but it is easy too , if you follow this vedic maths technique..
In order to multiply a number from 11 , You have to move from the number's unit's degit to the last digit ( i.e. from the right to left ) . You have to simply put the unit's digit as it is in the final answer, then you have to add the Unit's degit number with the number at Ten's place and put the answer (if the total of the Unit's and Ten's digit goes above 10 then you should place only the unit digit at the answer and carry the carryover Ten's digit of the answer to the next Hundred's digit and so on till you reach the last digit ) .

Theoritically its too difficult for You to understand if you don't love maths ( like 9/10 people ) ....
So, lets take some example, firstly we should take a two digit number like 35
35 x 11 = Put 5 as the unit digit of your final answer
next add "3" and "5" (as we should move in the left direction digit by digit) and put "8" as the Ten's digit of your final answer.
lastly put "3" as the hundredth and last digit of your final answer. ( this is done because you have already dealt with 5 , 5+3 and lastly 3 )
So the final answer is 385
35 x 11 = 385 ( 3 , 3+5 , 5 )

Next lets take another two digit number's example of 95 to show you a case if the total of the unit and tenth digit of the number get more than 10, here 9+5 > 10 , so here, calculation is a bit tricky.
So, we put the unit digit as the uint digit of the final answer ( as we did in the above example ) and then we add the two digit i.e 9 and 5 and put "4" as the Tenth digit of the answer ( Since, 9 + 5 = 14 , we put "4" in the tenth place of the final answer and carry 1 to further add with 9 )
Next, now we have to add the carryover of 1 with the last leftover digit of 9 and put the final answer as 1045.
This is how I did:
95 x 11 = ( 9 , 9+5 , 5 ) [ Since 9+5 = 14 we put 4 and carry 1 to add with the hundredth place number i.e. 9 )
so, 95 x 11 = ( 9 , 14 , 5)
= ( 9+1 , 4 , 5 )
= (10, 4 , 5 )
= 1045 [ Our final answer ]

Now, we should take a four digit number as our example, like 2478
So, 2478 x 11 = ( 2 , 2+4, 4+7, 7+8, 8 )
= (2 , 6 , 11 , 15 , 8 ) [here both 7+8 and 4+7 > 10, thus we'll carryover]
= (2 , 6 , 11+1, 5 , 8 ) [ we carry over the "1" from "15" to add it to "11"]
= (2 , 6 , 12 , 5 , 8)
= (2 , 6+1 , 2 , 5 ,8) [we carry over the "1" from "12" to add it to "6"]
=(2 , 7 , 2 , 5 , 8)
= 27258 [ Final Answer ]
You can do the above method in very few steps and mentally too, once you understand the concept and practise a bit.
Self-Exercises :-

a) 24 x 11 = ?
b) 56 x 11 = ?
c) 598 x 11 = ?
d) 4589 x 11 = ?
e) 732865 x 11 = ?

Be free to comment and clear your doubts in case you face any doubt .

You might also like this post: Easy way to multiply numbers around 100 ...

Sixteen ( 16 ) Sutras of Vedic Mathematics

2009-02-18T17:21:00.000+05:30

This are all the Sixteen Sutras or Aphorisms of Vedic Mathematics with their respective meanings. -

Sr No.	Sutras	Meaning
1.	Ekadhikina Purvena	By one more than the previous one
2.	Nikhilam Navatashcaramam Dashatah	All from 9 and the last from 10
3.	Urdhva-Tiryagbyham	Vertically and crosswise
4.	Paraavartya Yojayet	Transpose and adjust
5.	Shunyam Saamyasamuccaye	When the sum is the same that sum is zero.
6.	(Anurupye) Shunyamanyat	If one is in ratio, the other is zero
7.	Sankalana-vyavakalanabhyam	By addition and by subtraction
8.	Puranapuranabyham	By the completion or non-completion
9.	Chalana-Kalanabyham	Differences and Similarities
10.	Yaavadunam	Whatever the extent of its deficiency
11.	Vyashtisamanstih	Part and Whole
12.	Shesanyankena Charamena	The remainders by the last digit
13.	Sopaantyadvayamantyam	The ultimate and twice the penultimate
14.	Ekanyunena Purvena	By one less than the previous one
15.	Gunitasamuchyah	The product of the sum is equal to the sum of the product
16.	Gunakasamuchyah	The factors of the sum is equal to the sum of the factors
Know about Vedic Mathematics Homepage

Squaring of a number ending with 1 (one)

2009-02-18T17:10:00.000+05:30

This technique works well for squaring number ending with 1. If you multiply the numbers the traditional way you will see why this works.
For example:
   31²=
Firstly, subtract 1 from the number. The number now ends in zero and will be quite easy to square now.
   30²= 900 (3 x 3 x 10 x 10)
This is our sub-total.

Secondly, add together 30 and 31 -- the number we squared plus the number we want to square.
   30 + 31 = 61
Add this to our sub-total, 900, to get 961 (900 + 61) , which becomes the answer.
Note: For the second step you can simply double the number we squared, 30 x 2 and then add 1.

Another example is:

   121²=
   121 - 1 = 120
   120²= 14400 (12 x 12 x 10 x 10)
   120 + 121 = 241
   14400 + 241 = 14641 [Answer]

Self Exercises :-
a) 21² =
b) 41² =
c) 81² =
d) 141² =

About Vedic Mathematics

2009-02-17T17:54:00.000+05:30

Vedic Mathematics is an ancient knowledge comprising of 16 sutras or aphorisms related to mathematics, check out all the 16 Sutras of Vedic Mathematics. This set of sutras was extracted from the Hindu Vedas which were written around 1500-900 BC. The founder of Vedic Mathematics was Swami Sri Bharati Krishna Tirthaji Maharaja, a Hindu scholar and mathematician.

It is also believed that this knowledge laid down the foundation of algorithm, square roots, algebra, the concept of zero and various methods of calculations. If you master all the Sutras or aphorisms in the vedic mathematics, you can solve any mathematical problem be it - arithmetic, algebra, geometry, or trigonometry and that also ORALLY !!.