VERTICALLY AND CROSSWISE MULTIPLICATION

   Consider the conventional multiplication of two 2 digit numbers 12 and 23 
        shown below:
                                    12
                                        X  23       
                                              36       
                                     24x
                                                          276                      

                                    This is normally called long multiplication but
                                    actually the answer can be written straight down
                                    using the VERTICALLY AND CROSSWISE
                                    formula.
                                          

                                    There are 3 steps:

                       a) Multiply vertically on the left: 2 x 3= 6
                           This gives the first figure of the answer.
                      b) Multiply crosswise and add: 1 x 3 + 2 x 2 = 7
                           This gives the middle figure.
                      c) Multiply vertically on the right: 1 x 2 = 3
                             This gives the last figure of the
                             

• 21 x 26 = 546

The method is the same as above
except that we get a 2-figure number, 14, in the
middle step, so the 1 is carried over to the left
(4 becomes 5).

• 33 x 44 = 1452

  There may be more than one carry in a sum:

  

  Vertically on the left we get 12.
  Crosswise gives us 24, so we carry 2 to the left
  and mentally get 144.

  Then vertically on the right we get 12 and the 1
  here is carried over to the 144 to make 1452.

This is multiplication  of 2  digits numbers  .Now  we learn 3 digits multiplication

               3 Digits Multiplication

                Let us try to understand this by an example.

                  123 x321=????
                Step 1   We start from right  and multiply last digits of both numbers vertically

                        3x1 =3

               Step 2   Multiply last two digits crosswise  and   add  together  and write before step one figure

                            2x1+3x2=2 + 6 = 8

              Step 3  Multiply  first and last digits  crosswise and middle digit vertically   and add together and write  total before   
                          step 2 figure
                             1x1 +3x3 +2x2 =1+9+3=14

               Step 4   Multiply first two digits crosswise  and   add  together  and write before step 3 figure also add carry

                         2x1 +3x2+1 =9

              Step 5   Multiply first  digits of both numbers vertically and write before step 4 figure

                         1     2     3
                          I
                         3     2     1
                         3  9 14  8 3   1x3=3  
                  Our required answer is 39483

                                                                                 Practice Test

                                                    28 x89         28x62              56x48      236 x456    58x 78

                                                     259x 789      289 x89 *       87 x56     211 x879    25x89
                                          

                                                                                Hint  289 x089  
                                                                                          289
                                                                                      x  089

                                  0x2  /  2x8+8x0=16  /     2x9+8x8+0x9=82    /   8x9+8x9=144   / 9x9=81

                                                     16+9=25     /   82+15=97   /144+8 =152     /81  

                                                                                   =       25721

                                                                                                  

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