Vedic Mathematics ppt
SlideShare Explore You
Successfully reported this slideshow.
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 10-15 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,
- …\” />
Upcoming SlideShare
Loading in …5
×
- 162 Comments
- 181 Likes
- Statistics
- Notes
- prathap kumar , Superintendent Engineer at ApTrans co
Show More
No Downloads
No notes for slide
- 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 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.
- 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 sub-sutra 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
Recommended
-
Learning to Teach Online
Online Course – LinkedIn Learning
-
Communication in the 21st Century Classroom
Online Course – LinkedIn Learning
-
Office 2016 for Educators
Online Course – LinkedIn Learning
-
Thay đổi nhỏ để thành công lớn VHN
Vo Hieu Nghia
-
Squaring of numbers
Krishna Kumawat
-
Global Healthcare Report Q2 2019
CB Insights
-
Be A Great Product Leader (Amplify, Oct 2019)
Adam Nash
-
Trillion Dollar Coach Book (Bill Campbell)
Eric Schmidt
-
APIdays Paris 2019 – Innovation @ scale, APIs as Digital Factories\’ New Machi…
apidays
-
A few thoughts on work life-balance
Wim Vanderbauwhede
- English
- Español
- Português
- Français
- Deutsch
LinkedIn Corporation © 2020
Public clipboards featuring this slide
No public clipboards found for this slide
Select another clipboard
×
Looks like you’ve clipped this slide to already.
Create a clipboard
You just clipped your first slide!
Clipping is a handy way to collect important slides you want to go back to later. Now customize the name of a clipboard to store your clips.
Description
Visibility
Others can see my Clipboard
…\” /><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 ( 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
