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vedic addition \| vedic subtraction \| vedic multiplication \| vedic division

Vedic Mathematical Tables by “Nikhilam Sutra”
Mathematics tables can be constructed from "Nikhilam Sutra" of Thirthaji having a preliminary knowledge of mathematical Tables up to 5x5.

Mathematical Tables (6 - 10)
Step 1:	Take the difference of the number from 10 and write them as flags of the numbers.
Step 2:	Take the products of the flags and take it as units.
Step 3:	Subtract from the first number the flag of the second number and take it as tens for 9 x 8.
	Take the difference of 9, 8 from 10 We get 1 and 2 respectively. Write 1 and 2 as flag of the numbers 9 & 8.
	Take the product of 1 & 2 and get 1 x 2 = 2. Take it as units. Subtract 2 from 9 and get 9 – 2 = 7.
	Take 7 as tens place. Hence
	9 x 8 = 9¹ x 8² = 9 – 2, 1 x 2 = 72 7 x 9 = 7³ x 9¹ = 7 – 1, 3 x 1 = 63

Instructions: (x-a) (x-b) = x (x - a - b) + ab, where x = 10


Mathematical Tables (11 - 15)
Step1:	Take the difference of the numbers from 10 and write them as flags of the numbers.
Step 2:	Take the product of the flags and take it as units.
Step 3:	Add the flags of the second number to the first number and take it as units.

	For 12 x 13
	Take the difference of 12 and 13 from10. We get 2nd and 3rd respectively. Write 2 and 3 as flags of the numbers 12 and 13.
	Take the product of 2 and 3 and get 2x3=6. Take it as units.
	Add 3 to 12 and get 12+3=15. Take it as tens. Its value is 15 x 10 = 150
	12 x 13 = 12² x 13³ = 12 + 3, 2 x 3 = 156 12 x 14 = 12² x 14⁴ = 12 + 4, 2 x 4 = 168

Instructions: (x + a) (x + b) = x (x + a + b) + ab, where x =10


Mathematical Tables when one number is above 10 and the other number is below 10
Step 1:	Take the difference of the numbers from 10 and write them as top of the flags.
Step 2:	Add the second difference number to the first number and take it as tens.
Step 3:	Take the product of the flags and subtract it from the tens value.

	For 9 x 13
	Since 9is 1 less to 10. Write 1 as flags of 9. 13 is 3 more to 10. Write 3 as flags of 13. Add 3 to 9 we get 3 + 9 = 12.
	Take 12 as tens. Its value 120. Take the product of the flags. We get 1 x 3 = 3.
	Subtract 3 from the tens value. We get 120 – 3 = 117
	Hence 9 x 13 = 9-1 x 133 = (9+3)10, -1x3 = 120-3 = 117 7 x 16 = 7-3 x 166 = (7-6)10, -3x6= 130-18 = 112

Instructions:(x - a)(x – b) = x(x – a + b) – ab


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