Multiplication Area Model worksheet - Free Printable

The task involves solving multiplication problems using the area model. The area model is a visual representation that breaks down multiplication into smaller, more manageable parts by decomposing numbers into their place values (tens and ones). Let's solve each problem step by step.

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1. \( 34 \times 23 \)

#### Step 1: Decompose the numbers
- \( 34 = 30 + 4 \)
- \( 23 = 20 + 3 \)

#### Step 2: Set up the area model
The area model will have four sections:
- Top left: \( 30 \times 20 \)
- Top right: \( 30 \times 3 \)
- Bottom left: \( 4 \times 20 \)
- Bottom right: \( 4 \times 3 \)

#### Step 3: Calculate each section
1. \( 30 \times 20 = 600 \)
2. \( 30 \times 3 = 90 \)
3. \( 4 \times 20 = 80 \)
4. \( 4 \times 3 = 12 \)

#### Step 4: Add the results
\[ 600 + 90 + 80 + 12 = 782 \]

#### Final Answer:
\[ 34 \times 23 = 782 \]

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2. \( 40 \times 32 \)

#### Step 1: Decompose the numbers
- \( 40 = 40 \) (already in tens)
- \( 32 = 30 + 2 \)

#### Step 2: Set up the area model
The area model will have two sections for each row:
- Top left: \( 40 \times 30 \)
- Top right: \( 40 \times 2 \)

#### Step 3: Calculate each section
1. \( 40 \times 30 = 1200 \)
2. \( 40 \times 2 = 80 \)

#### Step 4: Add the results
\[ 1200 + 80 = 1280 \]

#### Final Answer:
\[ 40 \times 32 = 1280 \]

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3. \( 58 \times 27 \)

#### Step 1: Decompose the numbers
- \( 58 = 50 + 8 \)
- \( 27 = 20 + 7 \)

#### Step 2: Set up the area model
The area model will have four sections:
- Top left: \( 50 \times 20 \)
- Top right: \( 50 \times 7 \)
- Bottom left: \( 8 \times 20 \)
- Bottom right: \( 8 \times 7 \)

#### Step 3: Calculate each section
1. \( 50 \times 20 = 1000 \)
2. \( 50 \times 7 = 350 \)
3. \( 8 \times 20 = 160 \)
4. \( 8 \times 7 = 56 \)

#### Step 4: Add the results
\[ 1000 + 350 + 160 + 56 = 1566 \]

#### Final Answer:
\[ 58 \times 27 = 1566 \]

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4. \( 83 \times 19 \)

#### Step 1: Decompose the numbers
- \( 83 = 80 + 3 \)
- \( 19 = 10 + 9 \)

#### Step 2: Set up the area model
The area model will have four sections:
- Top left: \( 80 \times 10 \)
- Top right: \( 80 \times 9 \)
- Bottom left: \( 3 \times 10 \)
- Bottom right: \( 3 \times 9 \)

#### Step 3: Calculate each section
1. \( 80 \times 10 = 800 \)
2. \( 80 \times 9 = 720 \)
3. \( 3 \times 10 = 30 \)
4. \( 3 \times 9 = 27 \)

#### Step 4: Add the results
\[ 800 + 720 + 30 + 27 = 1577 \]

#### Final Answer:
\[ 83 \times 19 = 1577 \]

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5. \( 34 \times 44 \)

#### Step 1: Decompose the numbers
- \( 34 = 30 + 4 \)
- \( 44 = 40 + 4 \)

#### Step 2: Set up the area model
The area model will have four sections:
- Top left: \( 30 \times 40 \)
- Top right: \( 30 \times 4 \)
- Bottom left: \( 4 \times 40 \)
- Bottom right: \( 4 \times 4 \)

#### Step 3: Calculate each section
1. \( 30 \times 40 = 1200 \)
2. \( 30 \times 4 = 120 \)
3. \( 4 \times 40 = 160 \)
4. \( 4 \times 4 = 16 \)

#### Step 4: Add the results
\[ 1200 + 120 + 160 + 16 = 1496 \]

#### Final Answer:
\[ 34 \times 44 = 1496 \]

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6. \( 62 \times 15 \)

#### Step 1: Decompose the numbers
- \( 62 = 60 + 2 \)
- \( 15 = 10 + 5 \)

#### Step 2: Set up the area model
The area model will have four sections:
- Top left: \( 60 \times 10 \)
- Top right: \( 60 \times 5 \)
- Bottom left: \( 2 \times 10 \)
- Bottom right: \( 2 \times 5 \)

#### Step 3: Calculate each section
1. \( 60 \times 10 = 600 \)
2. \( 60 \times 5 = 300 \)
3. \( 2 \times 10 = 20 \)
4. \( 2 \times 5 = 10 \)

#### Step 4: Add the results
\[ 600 + 300 + 20 + 10 = 930 \]

#### Final Answer:
\[ 62 \times 15 = 930 \]

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Final Answers

\[
\boxed{
\begin{aligned}
1. & \ 34 \times 23 = 782 \\
2. & \ 40 \times 32 = 1280 \\
3. & \ 58 \times 27 = 1566 \\
4. & \ 83 \times 19 = 1577 \\
5. & \ 34 \times 44 = 1496 \\
6. & \ 62 \times 15 = 930 \\
\end{aligned}
}
\]