User:Ganesangopalakrishnan

MULTIPLICATION OF TWO NUMBERS

Multiplication of any n-digit number by another n-digit number which contains all the digits are only 9.

Let the number be xyzt...... (n digits) which is to be multiplied by another number  9999......(n - 9's)

Step 1 : First part of the Multiplication is {(xyzt.....) - 1}

Step 2: Second part of the Multiplication is [{9-x} {9-y} {9-z} {9-t}...........]

Example 1 : 8 × 9 = (8-1){9-(8-1)} = 72 Step 1 : 8 - 1 = 7 Step 2 : 9 - 7 = 2

Example 2 : 76 × 99 = 7524 Step 1 : 76 - 1 = 75 Step 2 : (9 - 7) (9 - 5) = 24 Combining both the results in Steps 1 and 2, we write 76 × 99 = 7524.

Example 3 : 874 × 999 = 873126 Step 1 : 874 - 1 = 873 Step 2 : (9 - 8) (9 - 7) (9 - 3) = 126 Combining both the results in Steps 1 and 2, we write 874 × 999 = 873126.

Example 4 : 586324 × 999999 = 586323413676 Step 1 : 586324 - 1 = 586323 Step 2 : (9 - 5) (9 - 8) (9 - 6) (9 - 3) (9 - 2) (9 - 3)= 413676 Combining both the results in Steps 1 and 2, we write 586324 × 999999 = 586323413676.