Lattice Method Multiplication Worksheet A - Practice 2-digit by 2-digit multiplication using the lattice method.

The image shows a worksheet titled "Lattice Method of Multiplication" for 2-digit by 2-digit multiplication problems. The lattice method is a visual and systematic way to multiply numbers, breaking down the process into smaller steps.

Steps to Solve Using the Lattice Method:

1. Draw the Lattice Grid:
- For a 2-digit by 2-digit multiplication, draw a 2x2 grid.
- Each cell in the grid will be divided diagonally to separate tens and ones.

2. Label the Grid:
- Write the digits of the first number (multiplicand) along the top of the grid.
- Write the digits of the second number (multiplier) along the right side of the grid.

3. Multiply Digits:
- Multiply each digit of the multiplicand by each digit of the multiplier.
- Write the product in the corresponding cell, with the tens digit above the diagonal and the ones digit below the diagonal.

4. Add Along Diagonals:
- Add the numbers along each diagonal, starting from the bottom-right corner.
- If the sum is a two-digit number, carry the tens digit to the next diagonal.

5. Write the Final Answer:
- Read the numbers along the left and bottom edges of the grid to form the final product.

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Solving Each Problem:

#### Problem 1: \( 27 \times 42 \)

1. Draw the Grid:
- A 2x2 grid.

2. Label the Grid:
- Top: 2, 7
- Right: 4, 2

3. Multiply:
- \( 2 \times 4 = 08 \) → Write 0 above, 8 below.
- \( 2 \times 2 = 04 \) → Write 0 above, 4 below.
- \( 7 \times 4 = 28 \) → Write 2 above, 8 below.
- \( 7 \times 2 = 14 \) → Write 1 above, 4 below.

4. Add Along Diagonals:
- Bottom-right diagonal: 4 → Write 4.
- Next diagonal: \( 8 + 4 = 12 \) → Write 2, carry 1.
- Next diagonal: \( 0 + 2 + 1 = 3 \) → Write 3.
- Top-left diagonal: 0 → Write 0.

5. Final Answer:
- Reading from left to bottom: \( 1134 \)

#### Problem 2: \( 45 \times 25 \)

1. Draw the Grid:
- A 2x2 grid.

2. Label the Grid:
- Top: 4, 5
- Right: 2, 5

3. Multiply:
- \( 4 \times 2 = 08 \) → Write 0 above, 8 below.
- \( 4 \times 5 = 20 \) → Write 2 above, 0 below.
- \( 5 \times 2 = 10 \) → Write 1 above, 0 below.
- \( 5 \times 5 = 25 \) → Write 2 above, 5 below.

4. Add Along Diagonals:
- Bottom-right diagonal: 5 → Write 5.
- Next diagonal: \( 0 + 0 = 0 \) → Write 0.
- Next diagonal: \( 8 + 2 + 1 = 11 \) → Write 1, carry 1.
- Top-left diagonal: \( 0 + 2 + 1 = 3 \) → Write 3.

5. Final Answer:
- Reading from left to bottom: \( 1125 \)

#### Problem 3: \( 13 \times 64 \)

1. Draw the Grid:
- A 2x2 grid.

2. Label the Grid:
- Top: 1, 3
- Right: 6, 4

3. Multiply:
- \( 1 \times 6 = 06 \) → Write 0 above, 6 below.
- \( 1 \times 4 = 04 \) → Write 0 above, 4 below.
- \( 3 \times 6 = 18 \) → Write 1 above, 8 below.
- \( 3 \times 4 = 12 \) → Write 1 above, 2 below.

4. Add Along Diagonals:
- Bottom-right diagonal: 2 → Write 2.
- Next diagonal: \( 4 + 8 = 12 \) → Write 2, carry 1.
- Next diagonal: \( 6 + 1 + 1 = 8 \) → Write 8.
- Top-left diagonal: 0 → Write 0.

5. Final Answer:
- Reading from left to bottom: \( 832 \)

#### Problem 4: \( 97 \times 32 \)

1. Draw the Grid:
- A 2x2 grid.

2. Label the Grid:
- Top: 9, 7
- Right: 3, 2

3. Multiply:
- \( 9 \times 3 = 27 \) → Write 2 above, 7 below.
- \( 9 \times 2 = 18 \) → Write 1 above, 8 below.
- \( 7 \times 3 = 21 \) → Write 2 above, 1 below.
- \( 7 \times 2 = 14 \) → Write 1 above, 4 below.

4. Add Along Diagonals:
- Bottom-right diagonal: 4 → Write 4.
- Next diagonal: \( 8 + 1 = 9 \) → Write 9.
- Next diagonal: \( 7 + 2 + 1 = 10 \) → Write 0, carry 1.
- Top-left diagonal: \( 2 + 2 + 1 = 5 \) → Write 5.

5. Final Answer:
- Reading from left to bottom: \( 3104 \)

#### Problem 5: \( 38 \times 16 \)

1. Draw the Grid:
- A 2x2 grid.

2. Label the Grid:
- Top: 3, 8
- Right: 1, 6

3. Multiply:
- \( 3 \times 1 = 03 \) → Write 0 above, 3 below.
- \( 3 \times 6 = 18 \) → Write 1 above, 8 below.
- \( 8 \times 1 = 08 \) → Write 0 above, 8 below.
- \( 8 \times 6 = 48 \) → Write 4 above, 8 below.

4. Add Along Diagonals:
- Bottom-right diagonal: 8 → Write 8.
- Next diagonal: \( 8 + 8 = 16 \) → Write 6, carry 1.
- Next diagonal: \( 3 + 1 + 4 = 8 \) → Write 8.
- Top-left diagonal: 0 → Write 0.

5. Final Answer:
- Reading from left to bottom: \( 608 \)

#### Problem 6: \( 81 \times 43 \)

1. Draw the Grid:
- A 2x2 grid.

2. Label the Grid:
- Top: 8, 1
- Right: 4, 3

3. Multiply:
- \( 8 \times 4 = 32 \) → Write 3 above, 2 below.
- \( 8 \times 3 = 24 \) → Write 2 above, 4 below.
- \( 1 \times 4 = 04 \) → Write 0 above, 4 below.
- \( 1 \times 3 = 03 \) → Write 0 above, 3 below.

4. Add Along Diagonals:
- Bottom-right diagonal: 3 → Write 3.
- Next diagonal: \( 4 + 4 = 8 \) → Write 8.
- Next diagonal: \( 2 + 2 + 0 = 4 \) → Write 4.
- Top-left diagonal: \( 3 + 0 = 3 \) → Write 3.

5. Final Answer:
- Reading from left to bottom: \( 3483 \)

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Final Answers:

1. \( 27 \times 42 = 1134 \)
2. \( 45 \times 25 = 1125 \)
3. \( 13 \times 64 = 832 \)
4. \( 97 \times 32 = 3104 \)
5. \( 38 \times 16 = 608 \)
6. \( 81 \times 43 = 3483 \)

Boxed Final Answer:

\[
\boxed{1134, 1125, 832, 3104, 608, 3483}
\]