Partial Products Method

for Multiplication

 

The Partial Products Method one takes the base-ten decomposition of each factor and forms the products of all pairs of terms. Then these partial products are added together. The student text does not recommend any particular addition algorithm for this second stage. In the example at right traditional addition with carries done mentally is displayed, but your student may do that addition problem by the Partial Sums method.

Observe that the number of terms in the addition problem is the product of the numbers of digits in the factors. The reader may want to explore Partial Products on the example 121 * 121 and compare with the traditional method, or try 128 * 128 for an example that is less skewed towards the traditional method.

  
               83
               27
             ----
  80*20  ->  1600
  80* 7  ->   560
   3*20  ->    60
   3* 7  ->    21
             ----
             2241