निखिलम्‌ continued ...

Here is another of the special cases, re-iterating the rule to thumb explained in last post

998 x 996

In this case, the closest base is 1000
Thus like in previous example we write,

998:2
996:4
-------
/

For calculating the left part we can do, 998 + 4 = 994 or 996 + 2 = 994
For calculating the right part we do 4 x 2 = 8

998:2
996:4
-------
994/8

The answer is clearly not correct. Applying the rule again -
The number of digits on the right hand side of the slash should be equal to the number of zeroes in the base. Rest of the digits should be carried over and added to the digits on the left hand side.

Hence as the base is 1000, we need to have three digits on the right. So the correct answer is,

998:2
996:4
-------
994/008

998 x 996 = 994008

So far the base has been greater than the multiplier and multiplicand both. However, same method can be applied even if the base is less than both or either of them. Here are a couple of examples illustrating that -

(1) 1903 x 1004
Let's take base as 1000. So we can write,

1903:903
1004: 4
-------
/

For calculating the left part we can do, 1903 + 4 = 1907 ( or 1004 + 903 = 1907, which is too much of a work :))
For calculating the right part we do 903 x 4 = 3612
Thus we can write,

1903:903
1004: 4
------------
1907/₃612

According to the rule, we can't have more than 3 digits on the right side of the slash as the base is 1000. So we carry the 3 over to the left side, giving us -

1903:903
1004: 4
------------
1910/612

1903 x 1004 = 1910612

(2) 18 x 7
Let's take base as 10. So we get -

18:8
7: 3
-------
/

For calculating the left part we can do, 7 + 8 = 15 or 18 + 3 = 15
For calculating the right part we do 8 x 3 = 24
Thus we can write,

18:8
7: 3
-------
15/ ₂4

Here we need to carry over the 2 to the left to get -

18:8
7: 3
-------
13/4

But again the final answer is not in the form we want.
If we refer to last post, we have said that the value of the number to the left hand side of the slash is actually that number multiplied by the base. Thus

13/4 = (13 x 10) + 4 = 126

Hence,

18 x 7 = 126