Vedic Mathematics ppt
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Vedic Mathematics ppt<img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"What is Vedic Mathematics ?
 Vedic mathematics is the name given to the ancient system of mathematics which was r…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Why Vedic Mathematics?
 It helps a person to solve problems 1015 times faster.
 It reduces burden…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Base of Vedic Mathematics
 Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and the…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Base of Vedic Mathematics
 Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and the…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"EKĀDHIKENA PŪRVEŅA
 The Sutra (formula) Ekādhikena Pūrvena means:
 “ By one more than the previou…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"‘ Squaring of numbers ending in 5’.
 Conventional Method
 65 X 65
 6 5
 The Sutra (formula) NIKHILAM NAVATAS’CHARAMAM DASATAH means :
 Conventional Method
 97 X 94
 Conventional Method
 103 X 105
 Conventional Method
 103…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"ĀNURŨPYENA
 The Sutra (formula) ĀNURŨPYENA means :
 \’ proportionality \’
 or…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"ĀNURŨPYENA
 Conventional Method
 46 X 43
 4 6
 X 4 3
…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"ĀNURŨPYENA
 Conventional Method
 58 X 48
 5 8
 X 4 8
…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"URDHVA TIRYAGBHYAM
 The Sutra (formula)
 URDHVA TIRYAGBHYAM
 means :
…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Two digit multiplication by URDHVA TIRYAGBHYAM
 The Sutra (formula)
 URDHVA TIRYAGBHYAM
 Vedic Method
 4 6
 X 4 3
 Vedic Method
 103
 X 105 <img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET
 This sutra means whatever the extent of its deficiency, lessen it stil…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET
 98 2 = 9604
 The nearest power of 10 to 98 is 100. …\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET
 103 2 = 10609
 The nearest power of 10 to 103 is 10…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET
 1009 2 = 1018081
\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"SAŃKALANA – VYAVAKALANĀBHYAM
 The Sutra (formula)
 SAŃKALANA – VYAVAKALANĀBHYAM means :
 Example 1: 45x – 23y = 113 23x – 45y = 91
 Firstly add…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"SAŃKALANA – VYAVAKALANĀBHYAM
 Example 2:
 1955x – 476y = 2482 476x – 1955y = – 4913
 The Sutra (formula)
 ANTYAYOR DAŚAKE\’PI means :
 ‘ Num…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"ANTYAYOR DAŚAKE\'PI
 Vedic Method
 6 7
 X 6 3
 4 2 2 1
 892 X 808
 = 720736
 Try Yourself :
 398 …\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"LOPANA STHÂPANÂBHYÂM
 The Sutra (formula)
 LOPANA STHÂPANÂBHYÂM means :
 \’b…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"LOPANA STHÂPANÂBHYÂM
 Example :
 3x 2 + 7xy + 2y 2 + 11xz + 7yz + 6z 2
 Elim…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"GUNÌTA SAMUCCAYAH – SAMUCCAYA GUNÌTAH
 Example :
 3x 2 + 7xy + 2y 2 + 11xz + 7yz + 6z 2
 KRISHNA KUMAR KUMAWAT Teacher (MATHS)
 C.F.D.A.V. Public School,
 …\” />
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 1. VEDIC MATHEMATICS
 2. What is Vedic Mathematics ?
 Vedic mathematics is the name given to the ancient system of mathematics which was rediscovered from the Vedas.
 It’s 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 .
 3. Why Vedic Mathematics?
 It helps a person to solve problems 1015 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.
 4. Base of Vedic Mathematics
 Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and their corollaries derived from the Vedas.
 5. Base of Vedic Mathematics
 Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and their corollaries derived from the Vedas.
 6. EKĀDHIKENA PŪRVEŅA
 The Sutra (formula) Ekādhikena Pūrvena means:
 “ By one more than the previous one”.
 This Sutra is used to the
 ‘ Squaring of numbers ending in 5’.
 7. ‘ Squaring of numbers ending in 5’.
 Conventional Method
 65 X 65
 6 5
 X 6 5
 3 2 5
 3 9 0 X
 4 2 2 5
 Vedic Method
 65 X 65 = 4225
 ( \’multiply the previous digit 6 by one more than itself 7. Than write 25 )
 8. NIKHILAM NAVATAS’CHARAMAM DASATAH
 The Sutra (formula) NIKHILAM NAVATAS’CHARAMAM DASATAH means :
 “ all from 9 and the last from 10”
 This formula can be very effectively applied in multiplication of numbers, which are nearer to bases like 10, 100, 1000 i.e., to the powers of 10 (eg: 96 x 98 or 102 x 104).
 9. Case I : When both the numbers are lower than the base.
 Conventional Method
 97 X 94
 9 7
 X 9 4
 3 8 8
 8 7 3 X
 9 1 1 8
 Vedic Method
 97 3
 X 94 6
 9 1 1 8
 10. Case ( ii) : When both the numbers are higher than the base
 Conventional Method
 103 X 105
 103
 X 105
 5 1 5
 0 0 0 X
 1 0 3 X X
 1 0, 8 1 5
 Vedic Method
 For Example103 X 105
 103 3
 X 105 5
 1 0, 8 1 5
 11. Case III: When one number is more and the other is less than the base.
 Conventional Method
 103 X 98
 103
 X 98
 8 2 4
 9 2 7 X
 1 0, 0 9 4
 Vedic Method
 103 3
 X 98 2
 1 0, 0 9 4
 12. ĀNURŨPYENA
 The Sutra (formula) ĀNURŨPYENA means :
 \’ proportionality \’
 or
 \’ similarly \’
 This Sutra is highly useful to find products of two numbers when both of them are near the Common bases like 50, 60, 200 etc (multiples of powers of 10).
 13. ĀNURŨPYENA
 Conventional Method
 46 X 43
 4 6
 X 4 3
 1 3 8
 1 8 4 X
 1 9 7 8
 Vedic Method
 46 4
 X 43 7
 1 9 7 8
 14. ĀNURŨPYENA
 Conventional Method
 58 X 48
 5 8
 X 4 8
 4 6 4
 2 4 2 X
 2 8 8 4
 Vedic Method
 58 8
 X 48 2
 2 8 8 4
 15. URDHVA TIRYAGBHYAM
 The Sutra (formula)
 URDHVA TIRYAGBHYAM
 means :
 “ Vertically and cross wise”
 This the general formula applicable to all cases of multiplication and also in the division of a large number by another large number.
 16. Two digit multiplication by URDHVA TIRYAGBHYAM
 The Sutra (formula)
 URDHVA TIRYAGBHYAM
 means :
 “ Vertically and cross wise”
 Step 1 : 5×2=10, write down 0 and carry 1
 Step 2 : 7×2 + 5×3 = 14+15=29, add to it previous carry over value 1, so we have 30, now write down 0 and carry 3
 Step 3 : 7×3=21, add previous carry over value of 3 to get 24, write it down.
 So we have 2400 as the answer.
 17. Two digit multiplication by URDHVA TIRYAGBHYAM
 Vedic Method
 4 6
 X 4 3
 1 9 7 8
 18. Three digit multiplication by URDHVA TIRYAGBHYAM
 Vedic Method
 103
 X 105
 1 0, 8 1 5
 19. YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET
 This sutra means whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square of that deficiency.
 This sutra is very handy in calculating squares of numbers near(lesser) to powers of 10
 20. YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET
 98 2 = 9604
 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 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).
 21. YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET
 103 2 = 10609
 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), 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).
 22. YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET
 1009 2 = 1018081
 23. SAŃKALANA – VYAVAKALANĀBHYAM
 The Sutra (formula)
 SAŃKALANA – VYAVAKALANĀBHYAM means :
 \’by addition and by subtraction\’
 It can be applied in solving a special type of simultaneous equations where the x – coefficients and the y – coefficients are found interchanged.
 24. SAŃKALANA – VYAVAKALANĀBHYAM
 Example 1: 45x – 23y = 113 23x – 45y = 91
 Firstly add them,
 ( 45x – 23y ) + ( 23x – 45y ) = 113 + 91
 68x – 68y = 204
 x – y = 3
 Subtract one from other,
 ( 45x – 23y ) – ( 23x – 45y ) = 113 – 91
 22x + 22y = 22
 x + y = 1
 Rrepeat the same sutra,
 we get x = 2 and y = – 1
 25. SAŃKALANA – VYAVAKALANĀBHYAM
 Example 2:
 1955x – 476y = 2482 476x – 1955y = – 4913
 Just add,
 2431( x – y ) = – 2431
 x – y = 1
 Subtract,
 1479 ( x + y ) = 7395
 x + y = 5
 Once again add,
 2x = 4 x = 2
 subtract
 – 2y = – 6 y = 3
 26. ANTYAYOR DAŚAKE\’PI
 The Sutra (formula)
 ANTYAYOR DAŚAKE\’PI means :
 ‘ Numbers of which the last digits added up give 10.’
 This sutra is helpful in multiplying numbers whose last digits add up to 10(or powers of 10). The remaining digits of the numbers should be identical. For Example : In multiplication of numbers
 25 and 25,
 2 is common and 5 + 5 = 10
 47 and 43,
 4 is common and 7 + 3 = 10
 62 and 68,
 116 and 114.
 425 and 475
 27. ANTYAYOR DAŚAKE\’PI
 Vedic Method
 6 7
 X 6 3
 4 2 2 1
 The same rule works when the sum of the last 2, last 3, last 4 – – – digits added respectively equal to 100, 1000, 10000 — – – .
 The simple point to remember is to multiply each product by 10, 100, 1000, – – as the case may be .
 You can observe that this is more convenient while working with the product of 3 digit numbers
 28. ANTYAYOR DAŚAKE\’PI
 892 X 808
 = 720736
 Try Yourself :
 398 X 302
 = 120196
 795 X 705
 = 560475
 29. LOPANA STHÂPANÂBHYÂM
 The Sutra (formula)
 LOPANA STHÂPANÂBHYÂM means :
 \’by alternate elimination and retention\’
 Consider the case of factorization of quadratic equation of type
 ax 2 + by 2 + cz 2 + dxy + eyz + fzx
 This is a homogeneous equation of second degree in three variables x, y, z.
 The subsutra removes the difficulty and makes the factorization simple.
 30. LOPANA STHÂPANÂBHYÂM
 Example :
 3x 2 + 7xy + 2y 2 + 11xz + 7yz + 6z 2
 Eliminate z and retain x, y ;
 factorize
 3x 2 + 7xy + 2y 2 = (3x + y) (x + 2y)
 Eliminate y and retain x, z;
 factorize
 3x 2 + 11xz + 6z 2 = (3x + 2z) (x + 3z)
 Fill the gaps, the given expression
 (3x + y + 2z) (x + 2y + 3z)
 Eliminate z by putting z = 0 and retain x and y and factorize thus obtained a quadratic in x and y by means of Adyamadyena sutra.
 Similarly eliminate y and retain x and z and factorize the quadratic in x and z.
 With these two sets of factors, fill in the gaps caused by the elimination process of z and y respectively. This gives actual factors of the expression.
 31. GUNÌTA SAMUCCAYAH – SAMUCCAYA GUNÌTAH
 Example :
 3x 2 + 7xy + 2y 2 + 11xz + 7yz + 6z 2
 Eliminate z and retain x, y ;
 factorize
 3x 2 + 7xy + 2y 2 = (3x + y) (x + 2y)
 Eliminate y and retain x, z;
 factorize
 3x 2 + 11xz + 6z 2 = (3x + 2z) (x + 3z)
 Fill the gaps, the given expression
 (3x + y + 2z) (x + 2y + 3z)
 Eliminate z by putting z = 0 and retain x and y and factorize thus obtained a quadratic in x and y by means of Adyamadyena sutra.
 Similarly eliminate y and retain x and z and factorize the quadratic in x and z.
 With these two sets of factors, fill in the gaps caused by the elimination process of z and y respectively. This gives actual factors of the expression.
 32. Prepared By:
 KRISHNA KUMAR KUMAWAT Teacher (MATHS)
 C.F.D.A.V. Public School,
 Gadepan, Kota ( Rajasthan )
 India
 Ph. 09928407883
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…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Prepared By:
<img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"ANTYAYOR DAŚAKE\'PI
…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"ANTYAYOR DAŚAKE\'PI
<img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"SAŃKALANA – VYAVAKALANĀBHYAM
 This sutra means whatever the extent of its deficiency, lessen it stil…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET
<img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Two digit multiplication by URDHVA TIRYAGBHYAM
<img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Three digit multiplication by URDHVA TIRYAGBHYAM
<img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"NIKHILAM NAVATAS’CHARAMAM DASATAH
 <img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Case I : When both the numbers are lower than the base.
<img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Case ( ii) : When both the numbers are higher than the base
<img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Case III: When one number is more and the other is less than the base.
 Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and the…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"EKĀDHIKENA PŪRVEŅA
 Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and the…\” /><img src=\"https://www.slideshare.net/krishnakumawat/\" alt=\"Base of Vedic Mathematics