Complimentary Multiplication : Extension 1

Complimentary Multiplication : Extension-1

It is observed that in the previous post, the calculation for two-digit numbers are understood by many kids. However, with higher number of digits, some more clarity is needed. This post is added to have more clarity for specially Type II Corollary of previous post.

If we have more than two digits, then decimal complimentation can be observed in several ways.

Unit place digits are complimentary, like 1239 and 1231, 437 and 433, 254 and 256, ..

Last two digits are complimentary, like 1239 and 1261, 437 and 463, 254 and 246, …

Last three digits are complimentary, like 1239 and 1761, 4998 and 4002, …

This trend can continue and pair of numbers having similar characteristics can be explored, obtained and considered. It must be noted that in the pair of numbers, leaving complimentary digits, other digits are the same.

The method resembles that explained in the previous post. Product will contain two parts. Left part will be same part of the two numbers (to be multiplied) and one more than the same part. Right part is product of complimentary digits and number of digits in right part is twice the number of digits in the complimentation. The multiplication by the method explained in previous post is carried out below.

1239x1231 = 123x124 | 9x1 = 15252 | 09 = 1525209

437x433 = 43x44 | 7x3 = 1892 | 21 = 189221

254x256 = 25x26 | 4x6 = 650 | 24 = 65024

1239x1261 = 12x13 | 39x61 = 156 | 2379 = 1562379

437x463 = 4x5 | 37x63 = 20 | 2331 = 202331

254x246 = 2x3 | 54x46 = 6 | 2564 = 62564

1239x1761 = 1x2 | 239x761 = 2 | 181879 = 2181879

4998x4002 = 4x5 | 998x002 = 20 | 001996 = 20001996

This post is initiated and created at the behest of Diptasha Das, a great all round achiever in academics and sports.

Any kid can make comments for clarity and share it with their friends for getting more feedback.

Dr Himanshu Shekhar