Lattice Multiplication Worksheets - Free Printable

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 multi-digit multiplication. Below, I will solve each problem step by step.

---

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:
- Write the digits of 211 along the top row.
- Write the digits of 16 along the right column.

3. Multiply each pair of digits:
- Multiply each digit from the top by each digit from the right, placing the result in the corresponding cell.
- Split each product into tens and units (if necessary).

4. Add diagonally:
- Add the numbers along each diagonal, carrying over if necessary.

5. Read the final answer:
- The result is read from the bottom left to the top right.

Lattice Grid Setup:

```
2 1 1
┌─┬─┬─┐
1 │2│1│1│
├─┼─┼─┤
6 │6│6│6│
└─┴─┴─┘
```

- Top row (211): 2, 1, 1
- Right column (16): 1, 6

Fill in the cells:

- \( 2 \times 1 = 02 \) → Place 0 in the top-left, 2 in the bottom-right.
- \( 2 \times 6 = 12 \) → Place 1 in the top-left, 2 in the bottom-right.
- \( 1 \times 1 = 01 \) → Place 0 in the top-left, 1 in the bottom-right.
- \( 1 \times 6 = 06 \) → Place 0 in the top-left, 6 in the bottom-right.
- \( 1 \times 1 = 01 \) → Place 0 in the top-left, 1 in the bottom-right.
- \( 1 \times 6 = 06 \) → Place 0 in the top-left, 6 in the bottom-right.

Diagonal addition:

```
2 1 1
┌─┬─┬─┐
1 │0│0│0│
│2│1│1│
├─┼─┼─┤
6 │1│0│0│
│2│6│6│
└─┴─┴─┘
```

- Diagonal sums:
- Bottom-left diagonal: 0 → 0
- Next diagonal: 2 + 0 + 1 = 3 → 3
- Next diagonal: 1 + 1 + 0 + 0 = 2 → 2
- Next diagonal: 0 + 2 + 6 = 8 → 8
- Top-right diagonal: 6 → 6

Final Answer: \( 211 \times 16 = 3376 \)

---

#### 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 pair of digits:
- Fill in the cells with products split into tens and units.

4. Add diagonally:
- Sum the numbers along each diagonal.

Lattice Grid Setup:

```
3 5 5
┌─┬─┬─┐
1 │3│5│5│
├─┼─┼─┤
8 │2│4│4│
└─┴─┴─┘
```

- Top row (355): 3, 5, 5
- Right column (18): 1, 8

Fill in the cells:

- \( 3 \times 1 = 03 \)
- \( 3 \times 8 = 24 \)
- \( 5 \times 1 = 05 \)
- \( 5 \times 8 = 40 \)
- \( 5 \times 1 = 05 \)
- \( 5 \times 8 = 40 \)

Diagonal addition:

```
3 5 5
┌─┬─┬─┐
1 │0│0│0│
│3│5│5│
├─┼─┼─┤
8 │2│4│4│
│0│4│0│
└─┴─┴─┘
```

- Diagonal sums:
- Bottom-left diagonal: 0 → 0
- Next diagonal: 3 + 0 + 4 = 7 → 7
- Next diagonal: 5 + 5 + 4 + 0 = 14 → Carry 1, write 4
- Next diagonal: 0 + 2 + 4 + 1 = 7 → 7
- Top-right diagonal: 4 → 4

Final Answer: \( 355 \times 18 = 6390 \)

---

#### 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 pair of digits:
- Fill in the cells with products split into tens and units.

4. Add diagonally:
- Sum the numbers along each diagonal.

Lattice Grid Setup:

```
1 2 3
┌─┬─┬─┐
4 │4│8│12│
├─┼─┼─┤
5 │5│10│15│
└─┴─┴─┘
```

- Top row (123): 1, 2, 3
- Right column (45): 4, 5

Fill in the cells:

- \( 1 \times 4 = 04 \)
- \( 1 \times 5 = 05 \)
- \( 2 \times 4 = 08 \)
- \( 2 \times 5 = 10 \)
- \( 3 \times 4 = 12 \)
- \( 3 \times 5 = 15 \)

Diagonal addition:

```
1 2 3
┌─┬─┬─┐
4 │0│0│1│
│4│8│2│
├─┼─┼─┤
5 │0│1│1│
│5│0│5│
└─┴─┴─┘
```

- Diagonal sums:
- Bottom-left diagonal: 0 → 0
- Next diagonal: 4 + 0 + 1 = 5 → 5
- Next diagonal: 8 + 2 + 5 + 0 = 15 → Carry 1, write 5
- Next diagonal: 0 + 1 + 1 + 1 = 3 → 3
- Top-right diagonal: 5 → 5

Final Answer: \( 123 \times 45 = 5535 \)

---

#### 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 pair of digits:
- Fill in the cells with products split into tens and units.

4. Add diagonally:
- Sum the numbers along each diagonal.

Lattice Grid Setup:

```
6 6 8
┌─┬─┬─┐
9 │54│54│72│
├─┼─┼─┤
2 │12│12│16│
└─┴─┴─┘
```

- Top row (668): 6, 6, 8
- Right column (92): 9, 2

Fill in the cells:

- \( 6 \times 9 = 54 \)
- \( 6 \times 2 = 12 \)
- \( 6 \times 9 = 54 \)
- \( 6 \times 2 = 12 \)
- \( 8 \times 9 = 72 \)
- \( 8 \times 2 = 16 \)

Diagonal addition:

```
6 6 8
┌─┬─┬─┐
9 │5│4│7│
│4│5│2│
├─┼─┼─┤
2 │1│2│1│
│2│1│6│
└─┴─┴─┘
```

- Diagonal sums:
- Bottom-left diagonal: 5 → 5
- Next diagonal: 4 + 1 + 2 = 7 → 7
- Next diagonal: 4 + 5 + 2 + 1 = 12 → Carry 1, write 2
- Next diagonal: 7 + 2 + 1 + 1 = 11 → Carry 1, write 1
- Next diagonal: 1 + 1 = 2 → 2
- Top-right diagonal: 6 → 6

Final Answer: \( 668 \times 92 = 61576 \)

---

#### 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 pair of digits:
- Fill in the cells with products split into tens and units.

4. Add diagonally:
- Sum the numbers along each diagonal.

Lattice Grid Setup:

```
1 3 2
┌─┬─┬─┐
3 │3│9│6│
├─┼─┼─┤
3 │3│9│6│
└─┴─┴─┘
```

- Top row (132): 1, 3, 2
- Right column (33): 3, 3

Fill in the cells:

- \( 1 \times 3 = 03 \)
- \( 1 \times 3 = 03 \)
- \( 3 \times 3 = 09 \)
- \( 3 \times 3 = 09 \)
- \( 2 \times 3 = 06 \)
- \( 2 \times 3 = 06 \)

Diagonal addition:

```
1 3 2
┌─┬─┬─┐
3 │0│0│0│
│3│9│6│
├─┼─┼─┤
3 │0│0│0│
│3│9│6│
└─┴─┴─┘
```

- Diagonal sums:
- Bottom-left diagonal: 0 → 0
- Next diagonal: 3 + 0 + 3 = 6 → 6
- Next diagonal: 9 + 6 + 9 + 0 = 24 → Carry 2, write 4
- Next diagonal: 6 + 3 + 2 = 11 → Carry 1, write 1
- Top-right diagonal: 6 → 6

Final Answer: \( 132 \times 33 = 4356 \)

---

#### 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 pair of digits:
- Fill in the cells with products split into tens and units.

4. Add diagonally:
- Sum the numbers along each diagonal.

Lattice Grid Setup:

```
8 4 1
┌─┬─┬─┐
4 │32│16│ 4│
├─┼─┼─┤
6 │48│24│ 6│
└─┴─┴─┘
```

- Top row (841): 8, 4, 1
- Right column (46): 4, 6

Fill in the cells:

- \( 8 \times 4 = 32 \)
- \( 8 \times 6 = 48 \)
- \( 4 \times 4 = 16 \)
- \( 4 \times 6 = 24 \)
- \( 1 \times 4 = 04 \)
- \( 1 \times 6 = 06 \)

Diagonal addition:

```
8 4 1
┌─┬─┬─┐
4 │3│2│ 4│
│1│6│ 0│
├─┼─┼─┤
6 │4│8│ 6│
│2│4│ 0│
└─┴─┴─┘
```

- Diagonal sums:
- Bottom-left diagonal: 3 → 3
- Next diagonal: 2 + 4 + 2 = 8 → 8
- Next diagonal: 1 + 6 + 8 + 4 = 19 → Carry 1, write 9
- Next diagonal: 6 + 4 + 1 = 11 → Carry 1, write 1
- Next diagonal: 0 + 0 + 1 = 1 → 1
- Top-right diagonal: 6 → 6

Final Answer: \( 841 \times 46 = 38686 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
&\text{c. } 211 \times 16 = 3376 \\
&\text{d. } 355 \times 18 = 6390 \\
&\text{e. } 123 \times 45 = 5535 \\
&\text{f. } 668 \times 92 = 61576 \\
&\text{g. } 132 \times 33 = 4356 \\
&\text{h. } 841 \times 46 = 38686 \\
\end{aligned}
}
\]