Is it possible to find the product of two mixed numbers by multiplying the whole number parts together, then multiplying the two fractional parts together, and finally adding the two products? use an example

No, an example would be 1 1/2* 1 1/2 or 3/2*3/2 if you did it the way mentioned above you would get 1*1+1/2*1/2 which is 1 1/4, however if we multiply correctly, 3/2*3/2 we actually get 9/4 which is equal to 2 1/4.