it says  "complete the area model" and above it it says 31 x 213

To complete an area model for multiplying \(31 \times 213\), we break down the numbers using their place values and then multiply each part separately. Here's how to approach it:

### Step 1: Break down the numbers
- \(31\) can be broken down into \(30\) and \(1\).
- \(213\) can be broken down into \(200\), \(10\), and \(3\).

### Step 2: Set up the area model grid
Create a grid with the parts of \(31\) on one side and the parts of \(213\) on the other:

|        | \(200\) | \(10\) | \(3\) |
|--------|---------|--------|-------|
| \(30\) |         |        |       |
| \(1\)  |         |        |       |

### Step 3: Multiply each part
Now, fill in the grid by multiplying the corresponding parts:

- \(30 \times 200 = 6000\)
- \(30 \times 10 = 300\)
- \(30 \times 3 = 90\)
- \(1 \times 200 = 200\)
- \(1 \times 10 = 10\)
- \(1 \times 3 = 3\)

So, the area model should look like this:

|        | \(200\) | \(10\) | \(3\) |
|--------|---------|--------|-------|
| \(30\) | 6000    | 300    | 90    |
| \(1\)  | 200     | 10     | 3     |

### Step 4: Add the products
Finally, add up all the products:

\[
6000 + 300 + 90 + 200 + 10 + 3 = 6603
\]

So, \(31 \times 213 = 6603\).

Would you like more details or have any questions? Here are some related questions for further practice:

1. How would you set up an area model for \(47 \times 156\)?
2. Can you break down \(245 \times 32\) using an area model?
3. What is the purpose of using area models for multiplication?
4. How can you verify your result after using an area model?
5. How does an area model help in understanding the distributive property?

**Tip:** The area model is a visual representation of the distributive property in multiplication, making it easier to see how each part of the numbers contributes to the final product.

Learn how to complete the area model for multiplication of 31 by 213 using a step-by-step guide. Understand the breakdown of numbers into place values and how to multiply each part separately. Suitable for Grades 4-6.

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