Fiona wants to multiply

Question

. She knows that one way to find this product is to add all of the partial products shown in the area model.

Enter values below to show Fiona's work.

A rectangle divided into 2 parts horizontally and 3 parts vertically, creating 6 smaller rectangles. The left side is labeled 5, 20. The top is labeled 400, 30, 1. Each of the 6 rectangles is labeled: 400 times 20, 30 times 20, 1 times 20, 400 times 5, 30 times 5, 1 times 5.
Clear Check
Partial products of


5





Partial products of

Answer 1

To help Fiona find the product using the area model, we can first label the partial products from each rectangle as indicated in your description. It appears Fiona is multiplying a number (which can be inferred to be 5 and some quantities on top labeled as 400, 30, and 1) by another one (the left side labeled as 5, 20).

Here's how to break this down:

Area Model Representation

• The left side represents the two parts (5 and 20).
• The top represents the three parts (400, 30, and 1).

Calculating the Partial Products

1. For 20:

   • \( 400 \times 20 = 8000 \)
   • \( 30 \times 20 = 600 \)
   • \( 1 \times 20 = 20 \)

   Total for 20:
   \[ 8000 + 600 + 20 = 8620 \]

2. For 5:

   • \( 400 \times 5 = 2000 \)
   • \( 30 \times 5 = 150 \)
   • \( 1 \times 5 = 5 \)

   Total for 5:
   \[ 2000 + 150 + 5 = 2155 \]

Summary of Results

• Partial products of \( 20 \): 8000, 600, 20
• Partial products of \( 5 \): 2000, 150, 5

Final Calculation

Now we need to combine the totals from both calculations to find the overall product.

\[ 8620 + 2155 = 10775 \]

Completed Values

• Partial products of 5: 2000, 150, 5
• Partial products of 20: 8000, 600, 20

Thus, Fiona's final result for the product is 10,775.