3-Digit by 2-Digit Lattice Multiplication Worksheet

The task involves solving multiplication problems using the lattice method. The lattice method is a visual and systematic way to multiply numbers, especially useful for larger numbers. Below, I will solve each problem step by step.

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Step-by-Step Solution Using the Lattice Method

#### c. Find \( 211 \times 16 \)

1. Set up the lattice grid:
- For \( 211 \times 16 \), we need a 3x2 grid (since 211 has 3 digits and 16 has 2 digits).

2. Label the grid:
- Top row: 2, 1, 1 (digits of 211)
- Right column: 1, 6 (digits of 16)

3. Multiply each digit:
- Multiply each digit of 211 by each digit of 16 and place the results in the corresponding cells.
- Split each product into tens and units (top-left for tens, bottom-right for units).

| | 2 | 1 | 1 |
|-----|---|---|---|
| 1 | 2/0 | 1/0 | 1/0 |
| 6 | 1/2 | 0/6 | 0/6 |

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

Diagonals:
- Bottom-right: 0
- Next diagonal: 0 + 6 + 0 = 6
- Next diagonal: 1 + 6 + 0 = 7
- Next diagonal: 2 + 1 + 0 = 3
- Next diagonal: 2

5. Final answer:
- Reading from top-left to bottom-right: \( 3376 \)

Answer: \( 3376 \)

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#### d. Find \( 355 \times 18 \)

1. Set up the lattice grid:
- For \( 355 \times 18 \), we need a 3x2 grid.

2. Label the grid:
- Top row: 3, 5, 5
- Right column: 1, 8

3. Multiply each digit:

| | 3 | 5 | 5 |
|-----|---|---|---|
| 1 | 0/3 | 0/5 | 0/5 |
| 8 | 2/4 | 4/0 | 4/0 |

4. Add diagonally:

Diagonals:
- Bottom-right: 0
- Next diagonal: 5 + 0 + 0 = 5
- Next diagonal: 5 + 0 + 0 = 5
- Next diagonal: 3 + 4 + 4 = 11 (write 1, carry 1)
- Next diagonal: 2 + 4 + 1 = 7
- Next diagonal: 3

5. Final answer:
- Reading from top-left to bottom-right: \( 6390 \)

Answer: \( 6390 \)

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#### e. Find \( 123 \times 45 \)

1. Set up the lattice grid:
- For \( 123 \times 45 \), we need a 3x2 grid.

2. Label the grid:
- Top row: 1, 2, 3
- Right column: 4, 5

3. Multiply each digit:

| | 1 | 2 | 3 |
|-----|---|---|---|
| 4 | 0/4 | 0/8 | 1/2 |
| 5 | 0/5 | 1/0 | 1/5 |

4. Add diagonally:

Diagonals:
- Bottom-right: 2
- Next diagonal: 5 + 2 + 0 = 7
- Next diagonal: 8 + 0 + 5 = 13 (write 3, carry 1)
- Next diagonal: 4 + 0 + 1 + 1 = 6
- Next diagonal: 0

5. Final answer:
- Reading from top-left to bottom-right: \( 5535 \)

Answer: \( 5535 \)

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#### f. Find \( 668 \times 92 \)

1. Set up the lattice grid:
- For \( 668 \times 92 \), we need a 3x2 grid.

2. Label the grid:
- Top row: 6, 6, 8
- Right column: 9, 2

3. Multiply each digit:

| | 6 | 6 | 8 |
|-----|---|---|---|
| 9 | 5/4 | 5/4 | 7/2 |
| 2 | 1/2 | 1/2 | 1/6 |

4. Add diagonally:

Diagonals:
- Bottom-right: 2
- Next diagonal: 6 + 2 + 0 = 8
- Next diagonal: 4 + 4 + 2 + 1 = 11 (write 1, carry 1)
- Next diagonal: 5 + 4 + 2 + 1 = 12 (write 2, carry 1)
- Next diagonal: 5 + 1 + 1 = 7
- Next diagonal: 5

5. Final answer:
- Reading from top-left to bottom-right: \( 61576 \)

Answer: \( 61576 \)

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#### g. Find \( 132 \times 33 \)

1. Set up the lattice grid:
- For \( 132 \times 33 \), we need a 3x2 grid.

2. Label the grid:
- Top row: 1, 3, 2
- Right column: 3, 3

3. Multiply each digit:

| | 1 | 3 | 2 |
|-----|---|---|---|
| 3 | 0/3 | 0/9 | 0/6 |
| 3 | 0/3 | 0/9 | 0/6 |

4. Add diagonally:

Diagonals:
- Bottom-right: 6 + 6 = 12 (write 2, carry 1)
- Next diagonal: 9 + 9 + 1 = 19 (write 9, carry 1)
- Next diagonal: 3 + 3 + 1 = 7
- Next diagonal: 0

5. Final answer:
- Reading from top-left to bottom-right: \( 4356 \)

Answer: \( 4356 \)

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#### h. Find \( 841 \times 46 \)

1. Set up the lattice grid:
- For \( 841 \times 46 \), we need a 3x2 grid.

2. Label the grid:
- Top row: 8, 4, 1
- Right column: 4, 6

3. Multiply each digit:

| | 8 | 4 | 1 |
|-----|---|---|---|
| 4 | 3/2 | 1/6 | 0/4 |
| 6 | 4/8 | 2/4 | 0/6 |

4. Add diagonally:

Diagonals:
- Bottom-right: 4 + 6 = 10 (write 0, carry 1)
- Next diagonal: 4 + 4 + 1 = 9
- Next diagonal: 6 + 8 + 2 = 16 (write 6, carry 1)
- Next diagonal: 2 + 1 + 1 = 4
- Next diagonal: 3

5. Final answer:
- Reading from top-left to bottom-right: \( 38686 \)

Answer: \( 38686 \)

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Final Answers:

\[
\boxed{
\begin{aligned}
&\text{c. } 3376 \\
&\text{d. } 6390 \\
&\text{e. } 5535 \\
&\text{f. } 61576 \\
&\text{g. } 4356 \\
&\text{h. } 38686
\end{aligned}
}
\]