Partial-Products Multiplication
Partial-Product Multiplication is an alternative method for
solving multi-digit multiplication problems.
This is a strategy that is based on the distributive (grouping)
property of multiplication.
Information from the Algorithms Handbook of the Everyday Math Program
Lining up the problem
One of the key components
of this strategy is making
sure your partial products
are lined up properly.
Example from the Algorithms Handbook of the Everyday Math Program
Created by: Chris Cheatham and Maria Farmer WB 2010
Solving the Problem
First you start with the bottom Factor
and multiply that factor with the
largest digit from the top factor. In
this example that is the hundreds
place.
Then you multiply the same bottom
factor with the next biggest digit
from the top factor. In this example
that is the tens place.
Next you multiply the same bottom
factor with the number in the ones
place.
Example from the Algorithms Handbook of the Everyday Math Program
Created by: Chris Cheatham and Maria Farmer WB 2010
Solving the problem
After you have multiplied
each factor you need to add
up all of the partial
products to get your final
product.
Example from the Algorithms Handbook of the Everyday Math Program
Created by: Chris Cheatham and Maria Farmer WB 2010
Two by Two Multiplication
You still start by multiplying the bottom
factor to the top factor. Since the bottom
factor has two digits you need to start
with the highest digit from the bottom
factor and multiply it to the highest digit
from the top factor. In this example you
will multiply the tens place from the
bottom factor to the tens place of the top
factor.
Then you will multiply the tens place
from the bottom factor to the ones place
of the top factor.
Example from the Algorithms Handbook of the Everyday Math Program
Created by: Chris Cheatham and Maria Farmer WB 2010
Two by Two Multiplication
Next you move to the next
biggest digit in the bottom
factor and multiply that by
both digits from the top
factor. The tens place goes
first and then the ones.
Example from the Algorithms Handbook of the Everyday Math Program
Two by Two Multiplication
After you have multiplied
each factor you need to add
up all of the partial
products to get your final
product.
Example from the Algorithms Handbook of the Everyday Math Program
Created by: Chris Cheatham and Maria Farmer WB 2010