Chapter

This is a specific technique of multiplying any given number by 11

Example 1:  42 x 11

Step 1:  Make (n + 1) boxes for the answer where n equals the number of digits in the number to be multiplied by 11

Step 2:  Copy the left digit in the left box and right digit in the right box

Step 3:  Add the two digits (L + R) and insert the sum in the middle box

42 x 11 = 4/4 + 2/2

            = 462

If required carry over the tens digit to the left side by adding to the number on the left side.  For example 48 x 11 = 4/12/8 = 528.  (Carry the digit 1 of the number 12 and add it to the number 4 on the left hand side).

Example 2:  125 x 11 = 1/1 + 2/2 + 5/5

                                = 1375

Example 3:  3405 x 11 = 3/3 + 4/4 + 0/0 + 5/5

                                  = 37455

Example 4:  4876 x 11 = 4/12/15/13/6

                                  = 53636 (by carrying over the tenth digit in each case from right to left)

Step 1:  Writing the solution from the right side first digit is 6

Step 2:  6 + 7 = 13, keep 3 and carry over 1

Step 3:  7 + 8 + 1 (1 Carried over from the right) = 16.  Keep 6 carry 1

Step 4:  8 + 4 + 1 (Carried over from the right) = 13.  Keep 3 Carry 1

Step 5:  4 + 1 (Carried over from the right) = 5.

Step 6:  Final answer is 53636

Exercises:

36 x 11 = 396

88 x 11 = 968

91 x 11 = 1001

432 x 11 = 4752

3045 x 11 = 33495

7189 x 11 = 79079

81.46 x 1.1 = 89.606 (in case of decimals remove the decimals and multiply as above)

98.76 x 1.1 = 108.636

384.5 x 1.1 = 422.95

41.3 x 0.11 = 4.543

Corollary:

This method can also be used to calculate the higher powers of 11.

Example: 

11² = 11 x 11

      = 121

11³ = 121 x 11

      = 1331

11⁴ = 1331 x 11

      = 14641

11⁵ = 14641 x 11

      = 161051 and so on.