Lattice multiplication practice worksheet with six problems.

The task involves solving multiplication problems and filling in the results in a grid format. Let's solve each problem step by step.

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Problem 1:

$$
\begin{array}{r}
54 \\
\times 88 \\
\hline
\end{array}
$$

#### Step 1: Multiply 54 by 88.
- First, break down the multiplication:
$$
54 \times 88 = 54 \times (80 + 8) = (54 \times 80) + (54 \times 8)
$$

- Calculate \( 54 \times 80 \):
$$
54 \times 80 = 54 \times 8 \times 10 = 432 \times 10 = 4320
$$

- Calculate \( 54 \times 8 \):
$$
54 \times 8 = 432
$$

- Add the two results:
$$
4320 + 432 = 4752
$$

#### Final Answer for Problem 1:
$$
\boxed{4752}
$$

---

Problem 2:

$$
\begin{array}{r}
30 \\
\times 31 \\
\hline
\end{array}
$$

#### Step 1: Multiply 30 by 31.
- First, break down the multiplication:
$$
30 \times 31 = 30 \times (30 + 1) = (30 \times 30) + (30 \times 1)
$$

- Calculate \( 30 \times 30 \):
$$
30 \times 30 = 900
$$

- Calculate \( 30 \times 1 \):
$$
30 \times 1 = 30
$$

- Add the two results:
$$
900 + 30 = 930
$$

#### Final Answer for Problem 2:
$$
\boxed{930}
$$

---

Problem 3:

$$
\begin{array}{r}
56 \\
\times 49 \\
\hline
\end{array}
$$

#### Step 1: Multiply 56 by 49.
- First, break down the multiplication:
$$
56 \times 49 = 56 \times (50 - 1) = (56 \times 50) - (56 \times 1)
$$

- Calculate \( 56 \times 50 \):
$$
56 \times 50 = 56 \times 5 \times 10 = 280 \times 10 = 2800
$$

- Calculate \( 56 \times 1 \):
$$
56 \times 1 = 56
$$

- Subtract the two results:
$$
2800 - 56 = 2744
$$

#### Final Answer for Problem 3:
$$
\boxed{2744}
$$

---

Problem 4:

$$
\begin{array}{r}
77 \\
\times 33 \\
\hline
\end{array}
$$

#### Step 1: Multiply 77 by 33.
- First, break down the multiplication:
$$
77 \times 33 = 77 \times (30 + 3) = (77 \times 30) + (77 \times 3)
$$

- Calculate \( 77 \times 30 \):
$$
77 \times 30 = 77 \times 3 \times 10 = 231 \times 10 = 2310
$$

- Calculate \( 77 \times 3 \):
$$
77 \times 3 = 231
$$

- Add the two results:
$$
2310 + 231 = 2541
$$

#### Final Answer for Problem 4:
$$
\boxed{2541}
$$

---

Problem 5:

$$
\begin{array}{r}
49 \\
\times 51 \\
\hline
\end{array}
$$

#### Step 1: Multiply 49 by 51.
- First, break down the multiplication:
$$
49 \times 51 = 49 \times (50 + 1) = (49 \times 50) + (49 \times 1)
$$

- Calculate \( 49 \times 50 \):
$$
49 \times 50 = 49 \times 5 \times 10 = 245 \times 10 = 2450
$$

- Calculate \( 49 \times 1 \):
$$
49 \times 1 = 49
$$

- Add the two results:
$$
2450 + 49 = 2499
$$

#### Final Answer for Problem 5:
$$
\boxed{2499}
$$

---

Problem 6:

$$
\begin{array}{r}
75 \\
\times 33 \\
\hline
\end{array}
$$

#### Step 1: Multiply 75 by 33.
- First, break down the multiplication:
$$
75 \times 33 = 75 \times (30 + 3) = (75 \times 30) + (75 \times 3)
$$

- Calculate \( 75 \times 30 \):
$$
75 \times 30 = 75 \times 3 \times 10 = 225 \times 10 = 2250
$$

- Calculate \( 75 \times 3 \):
$$
75 \times 3 = 225
$$

- Add the two results:
$$
2250 + 225 = 2475
$$

#### Final Answer for Problem 6:
$$
\boxed{2475}
$$

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Final Answers:

1. \( \boxed{4752} \)
2. \( \boxed{930} \)
3. \( \boxed{2744} \)
4. \( \boxed{2541} \)
5. \( \boxed{2499} \)
6. \( \boxed{2475} \)

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These are the solutions to the given multiplication problems. Each step is detailed to ensure clarity.