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.

Recent math words

  1. What is an abacus? Definition and Chinese Abacus

    Jan 18, 22 08:00 AM

    What is an abacus? Learn quickly and easily to use an abacus to do math.

    Read More

  2. Width of an Object

    Jan 17, 22 09:15 AM

    What is the width of an object? Definition, explanation, and easy to understand real life examples.

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Share this page: