Fill in the Area Model - Math Worksheets - SplashLearn - Free Printable

The task involves completing the area model for multiplication problems. The area model is a visual representation of multiplication where the total area of a rectangle is divided into smaller rectangles, and the areas of these smaller rectangles are calculated to find the total product.

Problem 1: \( 15 \times 14 \)

#### Step-by-Step Solution:
1. Break down the numbers:
- \( 15 = 10 + 5 \)
- \( 14 = 10 + 4 \)

2. Divide the rectangle into smaller parts:
- The large rectangle is divided into four smaller rectangles:
- Top-left: \( 10 \times 10 \)
- Top-right: \( 10 \times 4 \)
- Bottom-left: \( 5 \times 10 \)
- Bottom-right: \( 5 \times 4 \)

3. Calculate the area of each smaller rectangle:
- \( 10 \times 10 = 100 \)
- \( 10 \times 4 = 40 \)
- \( 5 \times 10 = 50 \)
- \( 5 \times 4 = 20 \)

4. Sum the areas:
- Total area = \( 100 + 40 + 50 + 20 = 210 \)

5. Fill in the blanks:
- \( 15 \times 14 = 100 + 40 + 50 + 20 \)

Problem 2: \( 16 \times 15 \)

#### Step-by-Step Solution:
1. Break down the numbers:
- \( 16 = 10 + 6 \)
- \( 15 = 10 + 5 \)

2. Divide the rectangle into smaller parts:
- The large rectangle is divided into four smaller rectangles:
- Top-left: \( 10 \times 10 \)
- Top-right: \( 10 \times 5 \)
- Bottom-left: \( 6 \times 10 \)
- Bottom-right: \( 6 \times 5 \)

3. Calculate the area of each smaller rectangle:
- \( 10 \times 10 = 100 \)
- \( 10 \times 5 = 50 \)
- \( 6 \times 10 = 60 \)
- \( 6 \times 5 = 30 \)

4. Sum the areas:
- Total area = \( 100 + 50 + 60 + 30 = 240 \)

5. Fill in the blanks:
- \( 16 \times 15 = 100 + 50 + 60 + 30 \)

Problem 3: \( 18 \times 12 \)

#### Step-by-Step Solution:
1. Break down the numbers:
- \( 18 = 10 + 8 \)
- \( 12 = 10 + 2 \)

2. Divide the rectangle into smaller parts:
- The large rectangle is divided into four smaller rectangles:
- Top-left: \( 10 \times 10 \)
- Top-right: \( 10 \times 2 \)
- Bottom-left: \( 8 \times 10 \)
- Bottom-right: \( 8 \times 2 \)

3. Calculate the area of each smaller rectangle:
- \( 10 \times 10 = 100 \)
- \( 10 \times 2 = 20 \)
- \( 8 \times 10 = 80 \)
- \( 8 \times 2 = 16 \)

4. Sum the areas:
- Total area = \( 100 + 20 + 80 + 16 = 216 \)

5. Fill in the blanks:
- \( 18 \times 12 = 100 + 20 + 80 + 16 \)

Final Answers:

1. \( 15 \times 14 = 100 + 40 + 50 + 20 \)
2. \( 16 \times 15 = 100 + 50 + 60 + 30 \)
3. \( 18 \times 12 = 100 + 20 + 80 + 16 \)

\[
\boxed{100 + 40 + 50 + 20, 100 + 50 + 60 + 30, 100 + 20 + 80 + 16}
\]