 and then it says  multiply by showing two partial products

To multiply \(31 \times 213\) by showing two partial products, you can break down one of the numbers into two parts and then multiply each part separately before adding the results together.

### Step 1: Break down one number
We'll break down \(31\) into \(30 + 1\).

### Step 2: Multiply each part by \(213\)
Now, multiply each part separately by \(213\):

1. **First Partial Product:**
   \[
   30 \times 213 = 6390
   \]
   (We multiply \(213\) by \(30\) and get \(6390\)).

2. **Second Partial Product:**
   \[
   1 \times 213 = 213
   \]
   (We multiply \(213\) by \(1\) and get \(213\)).

### Step 3: Add the partial products
Finally, add the two partial products together:

\[
6390 + 213 = 6603
\]

So, \(31 \times 213 = 6603\) when using two partial products.

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

1. How would you find two partial products for \(56 \times 124\)?
2. Can you use a different breakdown of \(213\) instead of \(31\) to show two partial products?
3. Why is it useful to break down multiplication into partial products?
4. How would you explain the relationship between the partial products and the area model?
5. Can you demonstrate how to check your work after finding partial products?

**Tip:** Breaking down multiplication into partial products helps to simplify complex multiplications and makes it easier to spot errors or understand the process.

Learn how to multiply 31 by 213 using two partial products with a detailed step-by-step guide. This problem covers multiplication strategies, including breaking down numbers and adding partial products. Suitable for students in Grades 4-6.

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