Here are some Tips & Tricks to get your Mathematics more stronger
Some of the Sutras (Phrases) used in Vedic Mathematics :
Ekadhikena Purvena (One More than the Previous)
is useful in solving Special Multiplications like 25X25, 95X95, 105X105 etc
Special Divisons like 1 divided by 19, 29, 39, …. 199 etc.
2. Eka Nunena Purvena (One less than the Previous)
is useful in solving Special Multiplications like 777 X 999, 123456789X 999 999 999
3. Urdhva Tiryak bhyam (Vertically and Cross-wise)
is useful in General Multiplication of any number by any number.
4. Paravartya Yojayet (P-64) (Transpose and Apply)
is useful in solving Algebraic factors and divisions of some numbers etc.
5. Anurupyena (P-87) (Proportionately)
6. Adhyam-Adhyena, Antyam-antyena (P-87) (first by the first and the last by the last)
are useful in solving Quadratics
7. Lopana-stapana-bhyam (P-90) (by (alternate) Elimination and Retention)
is useful in factorizing long and harder quadratics..
8. Gunita-Samuchhayah Samuchhaya-gunitah which means
"The product of the sum of the coefficients in the factors is equal to
the sum of the coefficients in the product"
is a Sub-sutra of immense utility for the purpose of verifying the correctness of our answers in multiplications, divisions and factorisations:
9. Sunyam Samya samuccaye P-107 (when Samuccaya is the same, that Samuccaya is zero) Samuccaya is a technical term which has several meanings. This is useful in solving many complex factors and equations.
1st Example - 1 Divided by 19, 29, 39, …. 129 etc
Monday, July 28, 2008
Here are some Tips & Tricks to get your Mathematics more stronger
Some of the Sutras (Phrases) used in Vedic Mathematics :
Ekadhikena Purvena (One More than the Previous)
is useful in solving Special Multiplications like 25X25, 95X95, 105X105 etc
Special Divisons like 1 divided by 19, 29, 39, …. 199 etc.
2. Eka Nunena Purvena (One less than the Previous)
is useful in solving Special Multiplications like 777 X 999, 123456789X 999 999 999
3. Urdhva Tiryak bhyam (Vertically and Cross-wise)
is useful in General Multiplication of any number by any number.
4. Paravartya Yojayet (P-64) (Transpose and Apply)
is useful in solving Algebraic factors and divisions of some numbers etc.
5. Anurupyena (P-87) (Proportionately)
6. Adhyam-Adhyena, Antyam-antyena (P-87) (first by the first and the last by the last)
are useful in solving Quadratics
7. Lopana-stapana-bhyam (P-90) (by (alternate) Elimination and Retention)
is useful in factorizing long and harder quadratics..
8. Gunita-Samuchhayah Samuchhaya-gunitah which means
"The product of the sum of the coefficients in the factors is equal to
the sum of the coefficients in the product"
is a Sub-sutra of immense utility for the purpose of verifying the correctness of our answers in multiplications, divisions and factorisations:
9. Sunyam Samya samuccaye P-107 (when Samuccaya is the same, that Samuccaya is zero) Samuccaya is a technical term which has several meanings. This is useful in solving many complex factors and equations.
1st Example - 1 Divided by 19, 29, 39, …. 129 etc
To Divide 1 by numbers ending in 9 like 1 divided by 19, 29, 39, ….. 119 etc.
Some of these numbers like 19, 29, 59 are prime numbers and so cannot be factorised 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.
The Vedic Solution is obtained by applying the Sutra (theorem) Ekadhikena Purvena which when translated means "One more than the Previous"
Take for example 1 divided by 19. In the divisor 19, the previous is 1 and the factor is obtained by adding 1 to it which is 2. Similarly when we have to divide by 29, 39, … 119 the factors shall be 3,4,… 12 respectively. (Add 1 to the previous term in the divisor). After this divide 1 by the factor in a typical Vedic way and the answer is obtained in 1 step. Thus
1 divided by 19 = 0.0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1
1 divided by 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
2nd Example - Square of Numbers ending in 5
Squares of 25, 35, 45, 85, 95, 105, 195 etc can be worked out mentally
Again the Sutra used here is Ekadhikena Purvena which means, "One more than the previous."
The last term is always 5 and the Previous terms are 2, 3, 4, 8, 9, 10, 19 etc and we have to add 1 to them. Square of the last term 5 is always 25.
Thus the Square of 25 is 2x3/25 = 625
the Square of 35 is 3x4/25 = 1225
the Square of 45 is 4x5/25 = 2025
the Square of 85 is 8x9/25 = 7225
the Square of 95, 105, 195 can be obtained in the same way.
Use the above formula to find the products of
23 multiplied by 27; 44 multiplied by 46; 192 multiplied by 198 and so on.
THESE ARE SOME SIMPLE TRICKS BY WHICH YOU CAN GET YOUR MATHEMATICS MORE STRONGER.
FOR MORE RELATED TOPICS SEARCH THROUGH THE ADS..
Some of the Sutras (Phrases) used in Vedic Mathematics :
Ekadhikena Purvena (One More than the Previous)
is useful in solving Special Multiplications like 25X25, 95X95, 105X105 etc
Special Divisons like 1 divided by 19, 29, 39, …. 199 etc.
2. Eka Nunena Purvena (One less than the Previous)
is useful in solving Special Multiplications like 777 X 999, 123456789X 999 999 999
3. Urdhva Tiryak bhyam (Vertically and Cross-wise)
is useful in General Multiplication of any number by any number.
4. Paravartya Yojayet (P-64) (Transpose and Apply)
is useful in solving Algebraic factors and divisions of some numbers etc.
5. Anurupyena (P-87) (Proportionately)
6. Adhyam-Adhyena, Antyam-antyena (P-87) (first by the first and the last by the last)
are useful in solving Quadratics
7. Lopana-stapana-bhyam (P-90) (by (alternate) Elimination and Retention)
is useful in factorizing long and harder quadratics..
8. Gunita-Samuchhayah Samuchhaya-gunitah which means
"The product of the sum of the coefficients in the factors is equal to
the sum of the coefficients in the product"
is a Sub-sutra of immense utility for the purpose of verifying the correctness of our answers in multiplications, divisions and factorisations:
9. Sunyam Samya samuccaye P-107 (when Samuccaya is the same, that Samuccaya is zero) Samuccaya is a technical term which has several meanings. This is useful in solving many complex factors and equations.
1st Example - 1 Divided by 19, 29, 39, …. 129 etc
To Divide 1 by numbers ending in 9 like 1 divided by 19, 29, 39, ….. 119 etc.
Some of these numbers like 19, 29, 59 are prime numbers and so cannot be factorised 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.
The Vedic Solution is obtained by applying the Sutra (theorem) Ekadhikena Purvena which when translated means "One more than the Previous"
Take for example 1 divided by 19. In the divisor 19, the previous is 1 and the factor is obtained by adding 1 to it which is 2. Similarly when we have to divide by 29, 39, … 119 the factors shall be 3,4,… 12 respectively. (Add 1 to the previous term in the divisor). After this divide 1 by the factor in a typical Vedic way and the answer is obtained in 1 step. Thus
1 divided by 19 = 0.0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1
1 divided by 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
2nd Example - Square of Numbers ending in 5
Squares of 25, 35, 45, 85, 95, 105, 195 etc can be worked out mentally
Again the Sutra used here is Ekadhikena Purvena which means, "One more than the previous."
The last term is always 5 and the Previous terms are 2, 3, 4, 8, 9, 10, 19 etc and we have to add 1 to them. Square of the last term 5 is always 25.
Thus the Square of 25 is 2x3/25 = 625
the Square of 35 is 3x4/25 = 1225
the Square of 45 is 4x5/25 = 2025
the Square of 85 is 8x9/25 = 7225
the Square of 95, 105, 195 can be obtained in the same way.
Use the above formula to find the products of
23 multiplied by 27; 44 multiplied by 46; 192 multiplied by 198 and so on.
THESE ARE SOME SIMPLE TRICKS BY WHICH YOU CAN GET YOUR MATHEMATICS MORE STRONGER.
FOR MORE RELATED TOPICS SEARCH THROUGH THE ADS..
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