Multiplication Worksheet for practicing three-digit multiplication problems.

Problem Overview:

The task involves filling in the missing numbers in a series of "number machines" that multiply input numbers by specific values (e.g., 100, 500, 300, etc.). The goal is to use multiplication knowledge to determine the outputs for each input number.

Solution Approach:

For each number machine, we will:
1. Identify the multiplication factor (e.g., \( \times 100 \), \( \times 500 \), etc.).
2. Multiply each input number by the given factor to find the corresponding output.
3. Fill in the missing numbers accordingly.

Let's solve each section step by step.

---

Section 1: \( \times 100 \)

| Input | Output |
|-------|--------|
| 5 | 500 |
| 3 | 300 |
| 6 | 600 |
| 7 | 700 |
| 4 | 400 |
| 8 | 800 |
| 2 | 200 |

Explanation: Each input number is multiplied by 100. For example, \( 5 \times 100 = 500 \).

---

Section 2: \( \times 500 \)

| Input | Output |
|-------|--------|
| 5 | 2500 |
| 3 | 1500 |
| 6 | 3000 |
| 7 | 3500 |
| 4 | 2000 |
| 8 | 4000 |
| 2 | 1000 |

Explanation: Each input number is multiplied by 500. For example, \( 5 \times 500 = 2500 \).

---

Section 3: \( \times 300 \)

| Input | Output |
|-------|--------|
| 5 | 1500 |
| 3 | 900 |
| 6 | 1800 |
| 7 | 2100 |
| 4 | 1200 |
| 8 | 2400 |
| 2 | 600 |

Explanation: Each input number is multiplied by 300. For example, \( 5 \times 300 = 1500 \).

---

Section 4: \( \times 2 \)

| Input | Output |
|-------|--------|
| 200 | 400 |
| 500 | 1000 |
| 600 | 1200 |
| 400 | 800 |
| 800 | 1600 |
| 300 | 600 |
| 700 | 1400 |

Explanation: Each input number is multiplied by 2. For example, \( 200 \times 2 = 400 \).

---

Section 5: \( \times 4 \)

| Input | Output |
|-------|--------|
| 200 | 800 |
| 500 | 2000 |
| 600 | 2400 |
| 400 | 1600 |
| 800 | 3200 |
| 300 | 1200 |
| 700 | 2800 |

Explanation: Each input number is multiplied by 4. For example, \( 200 \times 4 = 800 \).

---

Section 6: \( \times 7 \)

| Input | Output |
|-------|--------|
| 200 | 1400 |
| 500 | 3500 |
| 600 | 4200 |
| 400 | 2800 |
| 800 | 5600 |
| 300 | 2100 |
| 700 | 4900 |

Explanation: Each input number is multiplied by 7. For example, \( 200 \times 7 = 1400 \).

---

Section 7: \( \times 800 \)

| Input | Output |
|-------|--------|
| 6 | 4800 |
| 2 | 1600 |
| 9 | 7200 |
| 5 | 4000 |
| 3 | 2400 |
| 7 | 5600 |
| 8 | 6400 |

Explanation: Each input number is multiplied by 800. For example, \( 6 \times 800 = 4800 \).

---

Section 8: \( \times 600 \)

| Input | Output |
|-------|--------|
| 6 | 3600 |
| 2 | 1200 |
| 9 | 5400 |
| 5 | 3000 |
| 3 | 1800 |
| 7 | 4200 |
| 8 | 4800 |

Explanation: Each input number is multiplied by 600. For example, \( 6 \times 600 = 3600 \).

---

Section 9: \( \times 900 \)

| Input | Output |
|-------|--------|
| 6 | 5400 |
| 2 | 1800 |
| 9 | 8100 |
| 5 | 4500 |
| 3 | 2700 |
| 7 | 6300 |
| 8 | 7200 |

Explanation: Each input number is multiplied by 900. For example, \( 6 \times 900 = 5400 \).

---

Final Answer:

\[
\boxed{
\begin{array}{c}
\text{Section 1: } 600, 700, 400, 800, 200 \\
\text{Section 2: } 1500, 3000, 3500, 2000, 4000, 1000 \\
\text{Section 3: } 900, 1800, 2100, 1200, 2400, 600 \\
\text{Section 4: } 400, 1000, 1200, 800, 1600, 600, 1400 \\
\text{Section 5: } 800, 2000, 2400, 1600, 3200, 1200, 2800 \\
\text{Section 6: } 1400, 3500, 4200, 2800, 5600, 2100, 4900 \\
\text{Section 7: } 4800, 1600, 7200, 4000, 2400, 5600, 6400 \\
\text{Section 8: } 3600, 1200, 5400, 3000, 1800, 4200, 4800 \\
\text{Section 9: } 5400, 1800, 8100, 4500, 2700, 6300, 7200 \\
\end{array}
}
\]