What is a Partial Product? Definition and Examples

A partial product is one part of the answer to a multiplication when one digit of a multiplicand is multiplied by another digit of a multiplier.

You get partial products when either the multiplicand or the multiplier has at least two digits. The one with more digits goes on top in vertical multiplication. In example #1 below, 12 is on top.

A couple of examples showing what the partial product is

Example #1

     12     (Multiplicand)
    × 3     (Multiplier)
 --------
       6     (Partial product: 3×2 = 6)

     30     (Partial product: 3×10 = 30)

 --------

     36    (Sum of the partial products)

When you multiply 12 by 3, the partial products are 6 and 30.

Example #2

   123     (Multiplicand)
    × 4     (Multiplier)
 --------
     12     (Partial product: 4×3 = 12)

     80     (Partial product: 4×20 = 80)

   400     (Partial product: 4×100 = 400)

 --------
   492    (Sum of the partial products)

When you multiply 123 by 4, the partial products are 12, 80, and 400.