Question

Use the area model to multiply 6(11d+f).
First, find the partial products.
11d f
6
Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.123
Now, write the product.
6(11d+f)=

Answer 1

To multiply \( 6(11d + f) \) using the area model, we can break it down into partial products.

1. **Set Up the Area Model:**
We will set up a rectangle where one side represents \( 6 \) and the other side represents \( (11d + f) \), breaking it down into two parts: \( 11d \) and \( f \).

2. **Draw the Rectangle:**
- The rectangle has a width of \( 6 \).
- The height is divided into two sections: one for \( 11d \) and the other for \( f \).

3. **Find the Partial Products:**
- The area of the rectangle for the portion with \( 11d \) is calculated as follows:
\[
6 \times 11d = 66d
\]

- The area of the rectangle for the portion with \( f \) is calculated as follows:
\[
6 \times f = 6f
\]

4. **Add the Partial Products Together:**
\[
66d + 6f
\]

5. **Write the Product:**
Putting it all together, we find that:
\[
6(11d + f) = 66d + 6f
\]

Thus, the final result is:
\[
\boxed{66d + 6f}
\]