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I see that you've uploaded an image showing real numbers and instructions to classify them by their types (sets of numbers to which they belong). I will help by categorizing each number.

Here are the categories of real numbers:
- **Natural Numbers (ℕ)**: Positive integers (1, 2, 3, …)
- **Whole Numbers (W)**: Natural numbers plus zero (0, 1, 2, 3, …)
- **Integers (ℤ)**: All whole numbers including negatives (…, -2, -1, 0, 1, 2, …)
- **Rational Numbers (ℚ)**: Numbers that can be expressed as fractions (includes terminating and repeating decimals)
- **Irrational Numbers (I)**: Numbers that cannot be expressed as fractions (non-terminating, non-repeating decimals)
- **Real Numbers (ℝ)**: All numbers on the number line, including both rational and irrational numbers.

Now I'll classify the numbers from your list:

1. **12**: 
   - Natural number (ℕ)
   - Whole number (W)
   - Integer (ℤ)
   - Rational number (ℚ)
   - Real number (ℝ)

2. **−15**: 
   - Integer (ℤ)
   - Rational number (ℚ)
   - Real number (ℝ)

3. **\( \frac{1}{2} \)**: 
   - Rational number (ℚ)
   - Real number (ℝ)

4. **3.18**: 
   - Rational number (ℚ) because it's a terminating decimal.
   - Real number (ℝ)

5. **\( \frac{8}{4} = 2 \)**: 
   - Natural number (ℕ)
   - Whole number (W)
   - Integer (ℤ)
   - Rational number (ℚ)
   - Real number (ℝ)

6. **9.3 (repeating)** \( 9.\overline{3} \):
   - Rational number (ℚ) because it's a repeating decimal.
   - Real number (ℝ)

7. **\( - \frac{7}{9} \)**: 
   - Rational number (ℚ)
   - Real number (ℝ)

8. **\( \sqrt{25} = 5 \)**: 
   - Natural number (ℕ)
   - Whole number (W)
   - Integer (ℤ)
   - Rational number (ℚ)
   - Real number (ℝ)

9. **\( \sqrt{3} \)**: 
   - Irrational number (I)
   - Real number (ℝ)

10. **\( - \sqrt{64} = -8 \)**: 
    - Integer (ℤ)
    - Rational number (ℚ)
    - Real number (ℝ)

11. **\( -\sqrt{12} \)**: 
    - Irrational number (I)
    - Real number (ℝ)

12. **\( \sqrt{13} \)**: 
    - Irrational number (I)
    - Real number (ℝ)

Let me know if you'd like any further details or explanations.

Here are 5 related questions to deepen your understanding:
1. What is the difference between rational and irrational numbers?
2. Can a repeating decimal be an irrational number?
3. Why is \( \sqrt{3} \) considered irrational while \( \sqrt{25} \) is not?
4. Are all integers also rational numbers? Why or why not?
5. How can you tell if a square root is irrational?

**Tip**: Remember, rational numbers either terminate or have repeating decimal patterns. If a decimal neither terminates nor repeats, it’s irrational!

Name all sets of numbers to which each real number belongs from the given list of numbers.

Learn how to classify real numbers into natural numbers, whole numbers, integers, rational numbers, and irrational numbers. This problem involves square roots, fractions, and terminating and repeating decimals. Suitable for students in Grades 7-9.

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