सूत्र १. एकाधिकेन पूर्वेण

The Sūtra: ekādhikena pūrveṇa (By one more than the one before) is used for addition (x + y) and subtraction (x - y) of numbers, and also discussed for squaring (x²) of numbers, that end with 5.
 
The technique for addition and subtraction used by this Sūtra is similar to the conventional methods, but replaces the 'carry-over' with a dot to the digit placed in the previous place to indicate its ekādhika, or +1. Due to this, the count never exceeds 10, which helps in counting fast and reduces the chances of error. However, the technique used by this Sūtra (ekādhikena pūrveṇa) should not be confused with Upasūtra 15. śūddha (discussed here ») which uses a completely different technique.
 
 
Addition of two (or more) numbers using Sūtra 1. ekādhikena pūrveṇa:
As an illustration, let us use this Sūtra for:
28 + 165 So, for a practitioner of Vedic Mathematics, for something like:
234 + 403 + 564 + 721 Again, for something like:
78924 + 27272 + 72684 Although, it does not provide a visible marked difference, this technique comes handy when we have too many numbers to deal with, like a shopping bill. However, this technique, not only drastically reduces the chances of error, it saves time since one never has to count more than 10.
 
And, this Sūtra obviously works because it is only a variation of the conventional method of addition, by using the 'Dot' as a graphic mnemonic device.
 
 
Subtraction of numbers using Sūtra 1. ekādhikena pūrveṇa:
As an illustration, let us use this Sūtra for:
34 - 18 So, for a practitioner of Vedic Mathematics, for something like:
5124 - 3608 Again, for something like:
78924 - 27272 Although this method can only subtract smaller numbers from bigger numbers, it can also be used in subtracting bigger numbers from smaller ones because x - y = -(y - x), as for something like:
234 - 7381  
And, this Sūtra obviously works because it is only a variation of the conventional method of subtraction, by using the 'Dot' as a graphic mnemonic device.
 
 
Squaring of numbers ending with 5 using Sūtra 1. ekādhikena pūrveṇa:
We have discussed this technique along with this Sūtra, as it is popularly referred. However, we recommend the corollary (Upasūtra 8. antyayordaśake'pi - discussed here ») for a more generalized approach.
 
As an illustration, let us use this Sūtra for:
15² Let us take another example, for something like:
35² So, for a practitioner of Vedic Mathematics, for something like:
9995² And, for something like:
10005² However, this technique may get cumbersome for bigger numbers - which is why it is discussed for 2-digit and 3-digit numbers. As an example, for something like:
7875² But, why does it work? For this Sūtra (ekādhikena pūrveṇa), let us consider the following:  
This Sūtra is also discussed for division by a number ending with 9. For example, 1/19. This discussion is merely an illustration, and with its limited domain of operability, we do not advice remembering patterns (at least for such limited usability).
 
Lastly, please remember that, as in any other form of mathematics, the mastery of Vedic Mathematics require practice and the judgement of applying the optimal method for a given scenario - a guideline of which, is presented in Applications »
 

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