Question

Use the area model to multiply 11(2+7z).
First, find the partial products.
2 7z
11
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.123
Now, write the product.
11

Answer 1

To use the area model to multiply \( 11(2 + 7z) \), we first break it down into its components, then find the partial products by creating a visual representation.

### Step 1: Set Up the Area Model

We can represent the expression \( 11(2 + 7z) \) as a rectangle where:
- The width is \( 11 \)
- The height is divided into two parts: \( 2 \) and \( 7z \)

### Step 2: Create the Area Model

```
+----------------+
| |
11 | 2 |
| |
+----------------+
| |
| 7z |
| |
+----------------+
```

### Step 3: Calculate the Partial Products

Now we will calculate the area of each rectangle:

1. **For the first rectangle (11 by 2):**
\[
11 \times 2 = 22
\]

2. **For the second rectangle (11 by 7z):**
\[
11 \times 7z = 77z
\]

### Step 4: Add the Partial Products

Now add the two partial products together:
\[
22 + 77z
\]

### Final Result

So, the product of \( 11(2 + 7z) \) is:
\[
\boxed{22 + 77z}
\]