Many ways to multiply: Russian Multiplication

           Russian Multiplication 

Here we are going to discuss Russian multiplication. This method is also known as binary multiplication. The simplicity of this type of multiplication stems from the fact that you are only halving and doubling numbers then adding. I will demonstrate by example.       

                                                             Multiply 17 X 18 = ?

1.)                  17 | 18                         first we place the two numbers side by side and separate them into 2                                          

                                                          columns

                                                                                                                                                                           

2.)                   17 | 18                        in this step we started with the column on the right and cut 18 in half 

                            |  9                         to get 9 then we cut the 9 in half and dropped the remainder to get 4

                            |  4                         then we cut the 4 in half to get 2 and the 2 was cut to get 1. we stopped

                            |  2                         here since we got to one this is as far as we need to go for this method

                            |  1                          to work

                                                                                                                                                                              

3.)                  17 | 18                         Here we took the left column and instead of halving we doubled the

                      34 |  9                          17 and got 34 and doubled the 34 and got 68 doubled the 68 and got

                      68 |  4                            136 and doubled the 136 to get 272. and we stopped here because

                    136 |  2                              the 272 is in the same row as the 1

                    272 |  1

                                                                                                                                                                       

4.)                  17 | 18                      

                      34 |  9                          What we did here was we looked in the right column and found all of the 

                      68 |  4                            even numbers that are in the right column and crossed out the 

                    136 |  2                             entire row that had an even number in the right column 

                    272 |  1

                                                                                                                                                                       

  5.)                17 | 18                                 

                      34 |  9            1             in this final step we took the numbers that were not crossed out in the

                      68 |  4            272           left column and added them together, and as you see we have the 

                    136 |  2            +34                so 17 X 18 =  306

                    272 |  1            306

Once again I am going to explain that although I use the words, " easy, quick, and simple" , everyone should pick the types and methods that work best for them. I feel it is important to understand that there are multiple ways of doing things in mathematics and when we stop searching for new approaches in math we stop the heart of mathematics and destroy what its was originally created to do. Which is explore, explain, examine, and expand our understanding of the world around us.