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Math for Kids23 chapters | 325 lessons

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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.

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:

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.

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.

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

Expanded form multiplication has some important steps that need to be followed to correctly complete the equation, or the multiplication problem you are figuring out. Let's use the problem 854 x 5 as an example in breaking down these steps.

Step 1: Expand the digit in the highest place value.

- With 854, start by expanding the 8 because it has the largest place value - it becomes 800.

Step 2: Multiply the expanded form of the highest place value.

- Multiply 800 by 5.

Step 3: Expand the digit in the next place value position.

- With 854, 5 is in the next place value, and because there is one place after the 5, it becomes 50.

Step 4: Multiply the expanded form of the second digit.

- Multiply 50 by 5; it equals 250.

Step 5: Continue expanding and multiplying each digit thereafter.

- With 854, 4 is the next place value, but since it is in the ones place and has no places after it, it remains a 4. Multiply 4 by 5 and get 20.

Step 6: Add the answers of all the expanded form multiplication problems to get the total answer.

- 4,000 + 250 + 20 = 4,270.

**Expanded form** uses **place value** to show the value of each individual digit in a number. Sometimes, breaking a number into expanded form can make it easier to multiply large numbers and you now know the six easy steps. Congratulations!

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Math for Kids23 chapters | 325 lessons

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