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Let's classify each number as either rational or irrational, and explain why:

1. **\(\frac{2}{3}\)**:
   - **Rational**. A rational number is any number that can be expressed as a fraction of two integers. Since \(\frac{2}{3}\) is a fraction, it is a rational number.

2. **\(\sqrt{25}\)**:
   - **Rational**. The square root of 25 is 5, which is a whole number (integer). All integers are rational numbers because they can be written as fractions (e.g., \(5 = \frac{5}{1}\)).

3. **\(-0.75\)**:
   - **Rational**. \(-0.75\) is a terminating decimal, and all terminating decimals are rational numbers because they can be written as fractions (in this case, \(-0.75 = \frac{-3}{4}\)).

4. **\(\sqrt{2}\)**:
   - **Irrational**. The square root of 2 cannot be expressed as a fraction of two integers, and its decimal expansion is non-terminating and non-repeating. Therefore, \(\sqrt{2}\) is an irrational number.

5. **7,548,123**:
   - **Rational**. This is a whole number (integer), and all integers are rational numbers because they can be expressed as fractions (e.g., \(7,548,123 = \frac{7,548,123}{1}\)).

### Summary:
- \(\frac{2}{3}\) → Rational
- \(\sqrt{25}\) → Rational
- \(-0.75\) → Rational
- \(\sqrt{2}\) → Irrational
- 7,548,123 → Rational

Would you like any further details or explanations? Here are five related questions to explore further:

1. What is the difference between rational and irrational numbers?
2. How can you prove that \(\sqrt{2}\) is irrational?
3. Can repeating decimals be classified as rational?
4. How do you classify the sum or product of rational and irrational numbers?
5. Are all square roots of perfect squares rational?

**Tip:** Any decimal that either terminates or repeats is always a rational number.

Classify each number as rational or irrational and explain: 2/3, √25, -0.75, √2, 7,548,123.

Understand how to classify numbers as rational or irrational with examples like 2/3, √25, -0.75, √2, and 7,548,123. Learn the key differences between rational and irrational numbers, including how to identify and explain them. Suitable for students in Grades 6-8.

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