Multiply by 11 - From Simple to Complex

Most learned the simple trick to multiply two digits by 11  in grade school.  But did you know you can save time and effort easily producing numbers like 435,471 times 11 into 4,790,181?



Simple Trick

• Add the tens digit to the ones digit and insert the answer between the numbers.  The three digit number is the answer.

          Format:  11 times TO (11 x TO)= T(T+O)O
                                                             (T=Tens digit, O=Ones digit)
          Real Number:  11 times 35  (11 x 35) =  3(3+5)5 = 385

How to Carry

• When it comes to the case when T+O>9, confusion can set in.  Just Carry the "1" that results in the tens digit sum onto (e.g., add) the "starting" tens digit

          Example:    11 times 39 (11 x 39) = 3(3+9)9 = 3(12)9 = (3+1)29 = 429

Longer Numbers Multiplied by 11

• The above rules come into play.  Simply add each number starting with the ones digit to the number to its right and each result gets written down as part of your answer.  Remember the carry rule above comes into play.

         Example w/o Carry:  11 times 50,432 (11 x 50432)
                                              **start on the right not how this is written
   ([nothing to the left]0+5)(5+0)(0+4)(4+3)(3+2)(2+0[nothing to the right])
                                                                                        =  554,752

         Example with Carry: 11 times 50,439 (note the 2 was changed to a 9 which will cause a carry situation)
   (0+5)(5+0)(0+4)(4+3)(3+9)(9+0) =
                                                               5547(12)9 = 554(7+1)29 = 554,829

Try it