Expanded Form Multiplication: Step-by-Step for Grades 3-5

Expanded form multiplication, also called the expanded algorithm, gives students in grades 3 through 5 a way to work through multi-digit problems without getting lost in every step of the traditional algorithm. Instead of tracking the whole problem at once, students break numbers into place value parts, multiply one part at a time, and then add the partial products. This post walks through the prerequisite skills, a step-by-step example, and a short video.

When my son was in third grade, he struggled with multi-digit multiplication.  The multiplication problems had too many digits, and the traditional algorithm was too complicated for him to keep track of all of the pieces.  I simplified the process for him by using the expanded multiplication method. 

Here is how we used the expanded multiplication method and place value strategies for multi-digit multiplication.

What Is the Expanded Algorithm for Multiplication?

The expanded algorithm for multiplication, also called expanded form multiplication or the expanded multiplication method, is a strategy where students break one or both numbers into their place values and multiply each part separately. Instead of working through the traditional algorithm all at once, students handle one piece at a time and then add the partial products at the end.

This approach works especially well for students in grades 3 through 5 who are overwhelmed by the traditional algorithm. It makes multiplication visible and keeps place-value thinking front and center throughout the problem.

Prerequisite Skills for Expanded Multiplication

Students need a solid understanding of a few skills to use the expanded multiplication method successfully.

Students need to be able to: 

• Write numbers in expanded form
• Multiply multi-digit by one-digit numbers (eg, 345 x 3)
• Multiply a multi-digit number by tens and hundreds (eg, 345 x 40 or 345 x 300) using quick place value strategies. Understanding why those quick strategies work is helpful, but functional knowledge is sufficient. 
• Line up numbers when adding larger numbers

Writing Numbers in Expanded Form

Writing numbers in expanded form is a fundamental skill that lays the foundation for performing expanded-form multiplication. It involves breaking down a number into its digits and expressing each digit in terms of its place value. 

For instance, 147 is 100 + 40 + 7. 

Multiply a Multi-Digit Number by Tens and Hundreds

Students must understand how to multiply a multi-digit number by tens and hundreds using a zero placeholder. 

For instance, students must know how to solve 178 x 30 by using 0 as a placeholder shortcut.  

Line Up Numbers when Adding

Since the calculations will result in larger numbers, students must be able to line up the digits when adding large numbers. 

For example, students must be able to line up 13,437 and 2,467 when adding vertically. 

How to Solve Math Problems Using the Expanded Multiplication Method

Here’s a step-by-step look at the process, using 681 × 38 as the example:

1. Break it down: Start by expanding one number.  In the example above, 38 becomes 30 (3 tens) and 8 (8 ones). 
2. Multiplication in Parts: Multiply 681 by 30 (or 3 tens) and place the result, 20,430, neatly below the problem. Then, multiply 681 by 8 (the ones place) and write down 5,448 under that problem.
3. Combining the Parts: Carefully add the two products. The sum of 20,430 and 5,448 is 25,878.

The expanded multiplication method works especially well for students who benefit from visual aids and a clear, step-by-step path through complex problems.

Here is a second example using a different problem, so you can see how the steps apply regardless of the numbers involved.

Why use the Expanded Multiplication Method? 

The expanded method works well for students who get overwhelmed by the traditional algorithm because it keeps each step visible and separate. It also reinforces the distributive property naturally — students see that 681 × 38 is really (681 × 30) + (681 × 8) — which lays the groundwork for algebra later on.

If students struggle with multi-digit multiplication, the expanded method gives them a manageable entry point before you introduce the standard algorithm.

For strategies on lining up and adding multi-digit numbers, see multi-digit addition strategies.

Multiplying multi-digit numbers by tens and hundreds using the expanded method not only strengthens students’ understanding of basic arithmetic but also lays the foundation for more advanced mathematical concepts. If you have students struggling with the traditional algorithm for multiplying multi-digit numbers, consider using the expanded multiplication method to simplify the problems.