Faster Subtraction
H.D. Motiramani
Addition is always easier than subtraction. For example, if We have to substract 5 from 8, conventional method is to do 8-5 to get 3. However, we can also get the answer if we add this 3 to 5 to make it 8. So we note that we need 3 becomes the answer. Because it was this number 3 needed to be added to 5to make this 5 to 8. We will follow this principle for our larger sums needing subtraction. Let us see the examples.
Example 1:
7543796
-4321684
--------------
3222112
For this answer 3222112, if we move from right to left, we see that 2 was added in 4 to make it 6, 1 was added in 8 to make it 9, again 1 was added in 6 to make it 7, likewise 2 was added in 1 to make it 3, 2 was added in 2 to make it 4, 2 was added in 3 to make it 5 and lastly 3 was needed to be added in 4 to make it 7. Thus we have subtracted 4321684 from the number 7543796 at top by way of adding each digit to the number which was to be subtracted.
In the above example each digit needing subtraction from upper digit was lower than upper digit. In some cases we will encounter the digit to be subtracted being larger than the upper digit. Let us see the example:
Example 2:
7543796
- 5524687
-----------
2019109
In this example, if we move from right to left, we come across the digit 7 needing to be subtracted from 6. Now 6 being lower than 7, we have to consider 6 as 16 and then we need 9 to be added to 7 to make it 16. The 6 at top, considered as 16 can be done only by carrying 1 from its left hand neighboring digit. So we need to consider previous digit which was 9 as 8 because 1 was given to 6 to make it 16. So wherever we will encounter this situation we will keep on taking 1 from previous digit or left hand neighbor, as we do in conventional method of subtraction. Now comes next digit 8 (9-1), so like in 1st example above we need zero to be added to 8 that needs subtraction. The process continues and we get the answer 2019109. Thus, addition method in subtraction yields faster result. However, it is a matter of practice and we do resort to conventional method of carrying from
neighbor whenever and wherever needed.
Let us see one more example:
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