How to Multiply Using Expanded Form

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  • 0:04 Streeeeetch It Out
  • 1:30 Expanded Form with…
  • 2:14 Important Steps
  • 3:35 Lesson Summary
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Lesson Transcript
Instructor: Rayna Cummings

Rayna has taught Elementary Education for 12 years (in both 1st, 2nd, and 3rd grades) and holds a M.Ed in Early Childhood Education from The Ohio State University

In this lesson, you will learn what expanded form means, how to convert numbers into expanded form, steps to successfully complete expanded form multiplication, and will view example problems using expanded form multiplication.

Streeeetch It Out

Have you ever taken Play-Doh or clay and stretched it out as far as you can? When we show numbers in expanded form, we are writing the value of each digit based upon its place value. Therefore, we are stretching out the number. For example:

Example of expanded form
Expanded form example

When you use expanded form, you have to know the place value of each digit. Place value is the value that a digit has based upon where it is located in a number. It is important to know the place value for each digit because that is what determines how many places after the digit need to be replaced with zeros. Let's see how this works with the number 245:

  • The 2 is in the hundreds place, so in expanded form it becomes 200 because there are two places after the 2 in 245 that need to be filled with zeros.
  • The 4 is in the tens place, so in expanded form it becomes 40 because there is one place after the 4 in 245 that needs to be filled with zeros.
  • The 5 is in the ones place. There are no places after it, so it remains a 5 because there are no zeros to add.

So, 245 becomes 200 + 40 + 5 in expanded form.

Expanded Form with Multiplication

Let's learn how to multiply using the 245 that we just put into expanded form. Just like stretching the Play-Doh out, we need to stretch out our multiplication problem in expanded form to figure it out. We want to multiply 245 x 6. So we can take 245 in its expanded form, or 200 + 40 + 5, and multiply each part of the number by 6.

Example of using expanded form multiplication
expanded form multiplication

After multiplying, just add all of the products together. 1,200 + 240 + 30 = 1,470.

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