Steps | 28 + 165 | ||
1. | Equate the digits of both the numbers by prefixing imaginary Zeroes in front, and separate the columns for each place. | In this case, 0 | 2 | 8 + 1 | 6 | 5 ------------ |
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2. | Sum the digits of each column, even if the the result is aśūddha (impure, to mean more than one digit holding a position). | In this case, 0 | 2 | 8 + 1 | 6 | 5 ------------ 1 | 8 | 13 |
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3. | Conduct a śūddhikaran to purify the number, so that every place is held by only one positive digit. | In this case, [1,8,13] has 13 in the One's place. So, only 3 can remain, and the 1 needs to be added to the next column, containing 8. Thus, [1,8,13] = 193, which is the answer! |
2 | 3 | 4 4 | 0 | 3 5 | 6 | 4 + 7 | 2 | 1 ------------------ 18 | 11 | 12 By śūddhikaran, [18,11,12] = 1922 Thus, 234 + 403 + 564 + 721 = 1922 |
7 | 8 | 9 | 2 | 4 2 | 7 | 2 | 7 | 2 + 7 | 2 | 6 | 8 | 4 ------------------------------ 17 | 18 | 18 | 18 | 10 Thus, 78924 + 27272 + 72684 = 178880 Note that, the 'carry-over' digit is taken into consideration for each columns. |
Steps | 34 - 18 | ||
1. | Equate the digits of both the numbers by prefixing imaginary Zeroes in front, and separate the columns for each place. | In this case, 3 | 4 - 1 | 8 ---------- |
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2. | Convert the digits as Rekhanks, and sum the digits of each column, even if the the result is aśūddha (impure, to mean more than one digit holding a position) | In this case, 3 | 4 + 1 | 8 ---------- 2 | 4 |
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3. | Conduct a śūddhikaran to purify the number, so that every place is held by only one positive digit. | In this case, [2,4] has 4 in the One's place. So, 1 needs to be taken from the previous digit and given to the next digit, which becomes (10 + 4) = (10 - 4) = 6. Thus, [2,4] = 16, which is the answer! |
5 | 1 | 2 | 4 + 3 | 6 | 0 | 8 ---------------------- 2 | 5 | 2 | 4 By śūddhikaran, [2,5,2,4] = 1516 Thus, 5124 - 3608 = 1516 |
7 | 8 | 9 | 2 | 4 + 2 | 7 | 2 | 7 | 2 ---------------------------- 5 | 1 | 6 | 15 | 2 Thus, 78924 - 27272 = 51652 Note that, the 'carry-over' digit is taken into consideration for each columns. Also, for negative results, it is replaced with the relative complement from the nearest m × 10 and m is carried-over, for consideration in next column. For example above, 2 + 7 = 5 and, 10 + 5 = 5. Hence, carry-over of 1. |
7 | 3 | 8 | 1 + 0 | 2 | 3 | 4 ---------------------- 7 | 1 | 4 | 17 Thus, 234 - 7381 = -(7381 - 234) = -7147 |
6 | 3 | 7 | 1 2 | 6 | 4 | 7 8 | 0 | 9 | 6 7 | 3 | 8 | 1 + 1 | 2 | 3 | 4 ----------------------- 5 | 16 | 7 | 3 Thus, 6371 - 2647 + 8096 - 7381 + 1234 = 5673 |
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