Vedic Maths

Vedic mathematics is the name
given to the ancient system of

mathematics which was
rediscovered from the Vedas.
Its a unique technique of

calculations based on simple
principles and rules , with which
any mathematical problem - be it
arithmetic, algebra, geometry or
trigonometry can be solved
mentally.
It helps a person to solve problems 10-15 times faster.
It reduces burden (Need to learn tables up to nine only)
It provides one line answer.
It is a magical tool to reduce scratch work and finger counting.

It increases concentration.
Time saved can be used to answer more questions.
Improves concentration.
Logical thinking process gets enhanced.

Vedic
Mathematics
now refers to a
set of sixteen
mathematical
formulae or
sutras and their
corollaries
derived from
the Vedas.
Vedic
Mathematics
now refers to a
set of sixteen
mathematical
formulae or
sutras and their
corollaries
derived from
the Vedas.
The Sutra This Sutra is
(formula) used to the
Ekdhikena
Prvena means: Squaring of
numbers ending
By one more than in 5.
the previous one.
Conventional Method Vedic Method
65 X 65 65 X 65 = 4225
65
X65
( 'multiply the
325 previous digit 6 by
390X one more than
4225 itself 7. Than write
25 )
The Sutra (formula) This formula can
NIKHILAM be very effectively
NAVATASCHARAM applied in
AM DASATAH multiplication of
means : numbers, which are
nearer to bases like
all from 9 and the 10, 100, 1000 i.e., to
last from 10 the powers of 10
(eg: 96 x 98 or 102
x 104).
97 X 94
97
X94 97 3
388 X 94 6
873X 9118
9118
Conventional Vedic Method
Method
103 X 105
For Example103 X 105
103
X 105
103 3
515
000X X 105 5
103XX 1 0, 8 1 5
1 0, 8 1 5
103 X 98
103 103 3
X 98 X 98 -2
824 1 0, 0 9 4
927X
1 0, 0 9 4
The Sutra (formula) This Sutra is highly
NURPYENA useful to find
means : products of two
numbers when
'proportionality ' both of them are
or near the Common
'similarly ' bases like 50, 60,
200 etc (multiples
of powers of 10).
46 X 43
46 46 -4
X43 X 43 -7
138 1978
184X
1978
58 X 48 58 8
58 X 48 -2
X48 2884
464
24 2X
2 8 84
The Sutra (formula) This the general
URDHVA formula applicable
TIRYAGBHYAM to all cases of
means : multiplication and
also in the division
Vertically and cross of a large number
wise by another large
number.
The Sutra (formula) Step 1: 52=10, write
down 0 and carry 1
URDHVA Step 2: 72 + 53 =
TIRYAGBHYAM 14+15=29, add to it
previous carry over
means : value 1, so we have
30, now write down 0
and carry 3
Vertically and cross Step 3: 73=21, add
wise previous carry over
value of 3 to get 24,
write it down.
So we have 2400 as
the answer.
Vedic Method
46
X43
1978
Vedic Method
103
X 105
1 0, 8 1 5
This sutra means This sutra is very
whatever the extent handy in
of its deficiency, calculating squares
lessen it still further of numbers
to that very extent; near(lesser) to
and also set up the powers of 10
square of that
deficiency.
The nearest power of 10 to 98 is 100.
Therefore, let us take 100 as our base.
Since 98 is 2 less than 100, we call 2

98 2
= 9604 as the deficiency.
Decrease the given number further by

an amount equal to the deficiency. i.e.,
perform ( 98 -2 ) = 96. This is the left
side of our answer!!.
On the right hand side put the square

of the deficiency, that is square of 2 =
04.
Append the results from step 4 and 5

to get the result. Hence the answer is
9604.
Note : While calculating step 5, the number of digits in the squared number (04)
should be equal to number of zeroes in the base(100).
The nearest power of 10 to 103 is 100.
Therefore, let us take 100 as our base.
Since 103 is 3 more than 100 (base),

103 = 2
10609 we call 3 as the surplus.
Increase the given number further by

an amount equal to the surplus. i.e.,
perform ( 103 + 3 ) = 106. This is the
left side of our answer!!.
On the right hand side put the square

of the surplus, that is square of 3 =
09.
Append the results from step 4 and 5

to get the result.Hence the answer is
10609.
Note : while calculating step 5, the number of digits in the squared number (09)
should be equal to number of zeroes in the base(100).
The Sutra (formula) It can be applied in
solving a special
SAKALANA
type of
VYAVAKALANBH simultaneous
YAM equations where
means : the x - coefficients
and the y -
'by addition and coefficients are
found
by subtraction'
interchanged.
Example 1: Firstly add them,
( 45x 23y ) + ( 23x 45y ) = 113 +
45x 23y = 113 91
23x 45y = 91 68x 68y = 204
xy=3
Subtract one from other,

( 45x 23y ) ( 23x 45y ) = 113
91
22x + 22y = 22
x+y=1
Repeat the same sutra,

Example 2: Just add,
2431( x y ) = - 2431
1955x 476y = 2482 x y = -1
476x 1955y = - 4913
Subtract,
1479 ( x + y ) = 7395
x+y=5
Once again add,
2x = 4 x=2
subtract
- 2y = - 6 y = 3
The Sutra (formula) This sutra is helpful in
multiplying numbers whose
ANTYAYOR last digits add up to 10(or
powers of 10). The
DAAKE'PI remaining digits of the
numbers should be
means : identical.
For Example: In
Numbers of multiplication of numbers
which the last 25 and 25,
2 is common and 5 + 5 = 10
digits added up
47 and 43,
give 10. 4 is common and 7 + 3 = 10
62 and 68,
116 and 114.
Vedic Method The same rule works
when the sum of the
last 2, last 3, last 4 - - -
digits added
respectively equal to
67 100, 1000, 10000 -- - - .
The simple point to
X63 remember is to multiply
each product by 10,
4221 100, 1000, - - as the
case may be .
You can observe that
this is more convenient
while working with the
product of 3 digit
Try Yourself :
892 X 808
= 720736 A) 398 X 302
= 120196
B) 795 X 705
= 560475
Consider the case of
factorization of
The Sutra (formula) quadratic equation of
LOPANA type
STHPANBHYM
ax2 + by2 + cz2 + dxy + eyz +
means : fzx
'by alternate This is a homogeneous

elimination and equation of second
degree in three
retention' variables x, y, z.
The sub-sutra removes

the difficulty and makes
Example : Eliminate z by putting z =
0 and retain x and y and
3x 2 + 7xy + 2y 2+ 11xz + 7yz + 6z 2 factorize thus obtained a
quadratic in x and y by
Eliminate z and retain x, y ;
means of Adyamadyena
factorize
sutra.
3x 2 + 7xy + 2y 2 = (3x + y) (x + 2y)
Eliminate y and retain x, z;

factorize
Similarly eliminate y and
3x 2 + 11xz + 6z 2 = (3x + 2z) (x + 3z)
retain x and z and factorize
the quadratic in x and z.
Fill the gaps, the given expression
With these two sets of
(3x + y + 2z) (x + 2y + 3z) factors, fill in the gaps
caused by the elimination
process of z and y
respectively. This gives
Example : Eliminate z by putting z =
0 and retain x and y and
3x 2 + 7xy + 2y 2+ 11xz + 7yz + 6z 2 factorize thus obtained a
quadratic in x and y by
Eliminate z and retain x, y ;
means of Adyamadyena
factorize
sutra.
3x 2 + 7xy + 2y 2 = (3x + y) (x + 2y)
Eliminate y and retain x, z;

factorize
Similarly eliminate y and
3x 2 + 11xz + 6z 2 = (3x + 2z) (x + 3z)
retain x and z and factorize
the quadratic in x and z.
Fill the gaps, the given expression
With these two sets of
(3x + y + 2z) (x + 2y + 3z) factors, fill in the gaps
caused by the elimination
process of z and y
respectively. This gives

Vedic Maths

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Vedic mathematics is the name

given to the ancient system of

Its a unique technique of

It reduces burden (Need to learn tables up to nine only)

It provides one line answer.

It is a magical tool to reduce scratch work and finger counting.

Time saved can be used to answer more questions.

Logical thinking process gets enhanced.

Since 98 is 2 less than 100, we call 2

Decrease the given number further by

On the right hand side put the square

Append the results from step 4 and 5

Since 103 is 3 more than 100 (base),

Increase the given number further by

On the right hand side put the square

Append the results from step 4 and 5

Subtract one from other,

Repeat the same sutra,

'by alternate This is a homogeneous

The sub-sutra removes

Eliminate y and retain x, z;

Eliminate y and retain x, z;

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