One More than the
Previous is a sutra useful in finding squares of numbers (like 25x25, 95x95,
105x105, 992x992 etc) and special divisions like 1 divided by 19, 29, 39, ….
199 etc. just in one step.
To divide 1 by numbers ending with 9
like 1 divided by 19, 29, 39, ….. 119 etc. is a tedious work, using
conventional method. Some of these numbers like 19, 29, and 59 are prime
numbers and so cannot be factorized and division becomes all the more difficult
and runs into many pages in the present conventional method and the chances of
making mistakes are many.
Method 1
For example, take 1/19.In the divisor(19),
previous one or the number before 9 is 1. By sutra,Ekaadhika or by adding 1
more to the previous one, we get 2. Lets call the previous one+1 (here 2) as
"x".In this method,we start from the end.There will be (divisor-1) terms
in the answer.Now,
·
Assign last number to be
1.Now,multiply it with "x".ie,
2 1
(1*x)|1
·
Now go on multiplying with
"x" for (divisor-1)/2 times (here,) [(19-1)/2],ie,
Result: 9 4 7 3 6 8 4 2 1
Process :(2*x+1)|(7*x)|(3*x+1)|[6*x+1
(Carry of last multiplication)]| (8*x)|(4*x)|(2*x)|(1*x)
·
In the next step, write the
compliment of 9 from the last number
onwards,(divisor-1)/2 times
Result : 0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1
Process :
(9-i)|(9-h)|(9-g)|(9-f)|(9-e)|(9-d)|(9-c)|(9-b)|(9-a)|i|h|g|f|e|d|c|b|a
·
Now, prefix 0., and this is your
final answer, more accurate than a value that your calculator or computer can
give.
=
0.0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1
So.try this yourself these 1/29,1/39,1/49.1/59.can also be
found in seconds,
For example,
1/29 = 0.0 3 4 4 8 2 7 5 8 6 2 0 6 8 9 6
5 5 1 7 2 4 1 3 7 9 3 1
Multiplication
Method: Value of 1 / 19
First
we recognize the last digit of the denominator of the type 1 / 9. Here the last
digit is 9. For a fraction of the form in whose denominator 9 is the last
digit, we take the case of 1 / 19 as follows: For 1 / 19, 'previous' of 19 is
1. And one more than of it is 1 + 1 = 2. Therefore 2 is the multiplier for the
conversion.
We
write the last digit in the numerator as 1 and follow the steps leftwards.
Step.
1 : 1
Step.
2 : 21(multiply 1 by 2, put to left)
Step.
3 : 421(multiply 2 by 2, put to left)
Step.
4 : 8421(multiply 4 by 2, put to left)
Step.
5 : 168421 (multiply 8 by
2=16, 1 carried over, 6 put to
left)
Step.
6 : 1368421 ( 6 X 2 =12,+1 =
13, 1 carried over, 3 put to
left )
Step.
7 : 7368421 ( 3 X 2, = 6 +1 = 7, put to left)
Step.
8 : 147368421 (as in the same
process)
Step.
9 : 947368421 ( Do – continue to step 18)
Step.
10 : 18947368421
Step.
11 : 178947368421
Step.
12 : 1578947368421
Step.
13 : 11578947368421
Step.
14 : 31578947368421
Step.
15 : 631578947368421
Step.
16 : 12631578947368421
Step.
17 : 52631578947368421
Step.
18 : 1052631578947368421
Now
from step 18 onward the same numbers and order towards left continue.
Thus
1 / 19 = 0.052631578947368421'
Method 2
Using the same method, we can find,1/7 and 1/39 etc.
Viz,
1/7 = (7/7) * (1/7) =7*(1/49) , where can be find out
by above method.
Also,1/13 = (3/3)*(1/13) =3*(1/39).
Nikhilam Navatashcaramam Dashatah
ALL FROM 9 AND THE LAST FROM 10
Use the formula all
from 9 and the last from 10, to perform instant subtractions.
For example 1000 - 357 = ? (subtraction
from 1000)
We simply take each
figure in 357 from 9 and the last figure from 10.
Step 1. 9-3 = 6
Step 2. 9-5 = 4
Step 3. 10-7 = 3
So the answer is 1000
- 357 = 643
And that's all there is to it!
This always works for
subtractions from numbers consisting of a 1 followed by nougats: 100; 1000;
10,000 etc.
Similarly 10,000 - 1049 = 8951
Urdhva-Tiryagbyham
Vertically and
clock wise:
Suppose you need 7*6
8 is 3 below 10 and 6 is 4 below 10.
Subtract (10-8)=2...............................
step -1 8
2
Subtract (10-6)= 4..............................
step -2 6
4
Subtract (8-4) or (6-2) [crosswise]
= 4...... step -3 4 8
Multiply (2*4) = 8.................................
step -4
Combine step 3 and 4
So Answer = 48
98*97
Subtract (100-98)=2..................step-1
Subtract (100-97)=3...................step-2
Subtract (97-2)=95....................step-3
Multiply (2*3) =06.....................step-4
Combine step 3 and 4
So Answer =9506
Example -1
You can get more information here......
Multiplication with a series of 9s
Multiplications
with numbers like 9, or 99, or 999, or 9999.....so on. It feels like if
multiplier is a big number, the calculation will be tough. But, with the help
of vedic math formulae, the multiplication is much easier for all '9' digits
multiplier. By using the method given below, we can multiply any number with
99,999,9999, etc. very quickly.
Please note that the methods or the vedic formulae, that we use in this
calculation, are "By one less than the one before" and "All
from 9 and the last from10".
There are three cases for the multiplication of numbers with a series of 9's.
- ·
Case
1: Multiplying a number with a multiplier having equal number of 9’s digits
(like 587 x 999)
Try these
- · Case
2: Multiplying a number with a multiplier having more number of 9’s digits (like 4678 x 999999)
- ·
Case
3: Multiplying a number with a multiplier having lesser number of 9’s digits (like 1628 x 99)
The method to solve 'Case 1' and 'Case 2' is the same, but for 'Case 3', the
method is different. Let us start with 'Case 1'.
- Multiplying a number with a multiplier having equal number of 9’s
digits
Multiply 587 by 999
587
x 999
------------
586 413
Solution is,
·
Let
us first do the calculation by conventional method to understand the solution.
Result will be 586413.
·
Split
the answer in two parts i.e. '586' and '413'.
·
Let's
see the first part of the result, i.e. 586. It is reduced by 1 from the number
being multiplied i.e. 587 - 1 = 586. {Vedic sutra "By one less than the
onebefore"}
·
Now
see the last part, i.e. 413. Subtract the multiplicand i.e. 587 from 1000
(multiplier + 1). Vedic Sutra applied here is "All from 9 and the last
from 10", and hence we substract 587 from 1000. So the outcome will be (9
-5 = 4, 9 - 8 = 1, 10 - 7 = 3) , and result is 413. Refer to image below for
more clarity:
1. Square of Numbers ending in 5.
Step -1 : Multiply the
figures (except the last 5) by one more than it.
Step -2 : Write (square
of 5)25 after it.
Example -Square -25
(25) 2 =
[2*(2+1)] 25
=[2*3]25
=625
(105)2 =
[10*(10*1)]25
=[10*11]25
=11025
Vedic Mathematics is very deep subject.There are unlimited benefits of it.It can help us in many ways.
·
It is very simple,
direct, totally unconventional, original and straight forward.
·
It encourages mental
calculations.
·
It enriches our
understanding of maths and enables us to see links and continuity between
different branches of maths.
· Vedic Maths system also
gives us a set of checking procedures for independent crosschecking of whatever
we do.
· It keeps the mind alert
and lively because of the element of choice and flexibility at each .
· Holistic development of
the human brain takes place through Vedic Mathematics along with
multidimensional thinking.
· Vedic Mathematics system
to quite an extent also helps us in developing our spiritual part of
personality.
· It can introduce
creativity in intelligent and smart students, while helping the slow-learners
grasp the basic concepts of mathematics. More and more use of Vedic math can
without any doubts generate interest in a subject that is generally dreaded by
children.
Thus, Vedic maths is considered to be more than the blessing of
the Veda for the entire humanity
Here are some important links that can help to understand deeply....
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