Steps | 99 × 97 | ||
1. | Consider the nearest power of 10 as the Base | In this case, the Base, closest to 97 and 99, is 100. | |
2. | Find the deficiencies of both the numbers, and represent as Rekhank for negative deficiencies. | In this case, the two deficiencies are: 100 - 99 = 1 and 100 - 97 = 3 |
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3. | Subtract the (Sum of deficiencies) from the Base | In this case, 100 - (1 + 3) = 100 - 4 = 96 |
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4. | Set-up as many Zeroes, as the Base | In this case, 100 has two Zeroes. So, we get 9600 |
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5. | Add the product of the deficiencies, to get the answer. | In this case, the product of the deficiencies is: 1 × 3 = 3 And, 9600 + 3 = 9603, which is the answer! |
The Base is 100 and, the deficiencies are: 100 - 98 = 2 and 100 - 103 = -3 = 3 So, sum of deficienies = 2 + 3 = 1 And, product of deficiencies = 2 × 3 = 6 Thus, 100 - 1 = 100 + 1 = 101 And, 101,00 + 6 = 10100 - 6 = 10094, which is the answer! |
The Base is 1000 and, 11 × 5 = 55 Also, 1000 - (11 + 5) = 994 And, 994000 + 55 = 993945 Thus, 989 × 1005 = 993,945 |
The Base is 100000 and, 12 × 4 = 48 Also, 100000 - (12 + 4) = 100016 And, 100016,00000 + 48 = 100016,00048 Thus, 100012 × 100004 = 10,001,600,048 |
Assuming two numbers (10n - a) and (10n - b) Then, (10n - a) × (10n - b) = 10n × 10n - a10n - b10n + ab = 10n × 10n - 10n(a + b) + ab = 10n (10n - (a + b)) + ab This is exactly what this Sūtra makes us do. |
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