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How to do Partial Products Multiplication

Updated on December 3, 2012

How to do Partial Products Multiplication

We are going to complete Partial Products with this problem
We are going to complete Partial Products with this problem
The Expanded Form of 234
The Expanded Form of 234

Partial Products Multiplication

Partial Products Multiplication is when you break the problem down into a series of multiplication problems instead of the traditional method. Some students find this method easier. I personally like it to explain why multi digit multiplication works and how it works. This is also one of thos methods that can be a better visual representation. In all these problems I have written the problem that I am doing on the side, but normally you would just do the multiplication portion without having to write the problem.

The first thing you need to understand is expanded form of a number. In the problem to the right you need to be able to comprehend that the 3 is really 30 and the 2 is really 200. Sometimes it is helpful to write out the expanded form of the number.

Add the partial products to get the completed product
Add the partial products to get the completed product

Step One: Break it into pieces

Since this problem only has one significant digit in the second number I will have 3 problems to multiply.

Remember the expanded form 200 +30 + 4, I need to multiply each significant digit by 50.

50 X 4

50 x 30

50 x 200

I complete these three problems in order and then add the partial products together in order to complete the finished product.


Traditional Method comes up with Same Answer

Traditional Method to Show same answer
Traditional Method to Show same answer

Partial Product for multi digit Multipliers

Each number multiplied by the ones digit of the multiplier
Each number multiplied by the ones digit of the multiplier
Partial Product Method of Multiplication
Partial Product Method of Multiplication

Let's Try a Harder Partial Product

Okay that was the basic partial product, but it was only with a 1 significant digit multiplier. Let's try a problem with two digit multiplier. This is the same thing but you need to think about the expanded form of both numbers

We are going to look at the problem 167 x 81

We need to think about the expanded form of both numbers

100 + 60 + 7

80 + 1

The first thing I am going to do is multiply 1 times each number in 167

1 x 7 = 7

1x 60 = 60

1x 100 = 100



Now to Multiply by the Tens Digit

We now need to multiply each digit by 80

80 x 7 = 560

80 x 60 = 4800

80 x 100 = 8000


Then we add all the partial products together in order to find the final product

One Last Tip

A Smart Top
A Smart Top
Partial Products down with a sideways paper to help alignment
Partial Products down with a sideways paper to help alignment

A Quick Top

Now not all my students are as neat as I am when they do their work. Some of my students really struggle to keep the numbers aligned. This is a simple easy top that will help them align their work. Remember this is where that flexible teacher part comes in.

Turn the Paper sideways! It works I promise. This works for all types of problems. Another suggestion is to use 1/2 inch grid paper. I frequently download grid paper off free template sites for my students to use.

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