Question

Use the area model to multiply 8
5

9
m+20+
1

3
n.
First, find the partial products. Write numbers as integers, decimals, or simplified proper or improper fractions.
5

9
m 20
1

3
n
8



Row, rectangle. Width. Height. Find the total area.. Areacolumn, missing side length.1234
Now, write the product.
8
5

9
m+20+
1

3
n=







Questions

Answer 1

To multiply \( 859(m + 20) + 13n \) by \( 8 \) using the area model, let's break it down step by step.

### Step 1: Breaking down the expression
We start by rewriting the expression in a clearer format:

\[
8 \cdot (859(m + 20) + 13n)
\]

This can be separated as:
\[
(8 \cdot 859(m + 20)) + (8 \cdot 13n)
\]

### Step 2: Calculate Partial Products
Now we compute each part separately.

1. **For \( 8 \cdot 859(m + 20) \)**:
- Distributing:
- \( 8 \cdot 859m + 8 \cdot 859 \cdot 20 \)
- Calculating:
- \( 8 \cdot 859 = 6872 \)
- \( 8 \cdot 20 = 160 \)
- Therefore, \( 8 \cdot 859(m + 20) = 6872m + 6872 \cdot 20 = 6872m + 32000 \)

2. **For \( 8 \cdot 13n \)**:
- Calculating:
- \( 8 \cdot 13 = 104 \)
- Thus, \( 8 \cdot 13n = 104n \)

### Step 3: Compile the Total Area
Now we can combine the products:

\[
6872m + 32000 + 104n
\]

### Step 4: Write the Final Product
Therefore, the final product of multiplying \( 859(m + 20) + 13n \) by \( 8 \) is:

\[
8 \cdot (859(m + 20) + 13n) = 6872m + 32000 + 104n
\]

This provides the full result in terms of \( m \) and \( n \).

#### Summary:
- Partial Products:
- \( 8 \cdot 859m = 6872m \)
- \( 8 \cdot 20 \cdot 859 = 32000 \)
- \( 8 \cdot 13n = 104n \)

- Final Product:
- \( 6872m + 32000 + 104n \)

Let me know if you have any further questions or clarifications!