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)

Since multiplication is commutative, it would not matter if you put the multiplier on top. Just make sure the bigger number is in top! 

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.

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