https://file.aiquickdraw.com/mathbot/file/1726165093950gwq6vacc.jpg

Let's classify the numbers as rational or irrational based on the provided image:

1. **2**: This is a rational number because it can be expressed as the fraction \( \frac{2}{1} \), which is a ratio of two integers.

2. **\( \pi \)**: This is an irrational number. \( \pi \) cannot be expressed as a fraction of two integers and its decimal expansion is non-terminating and non-repeating.

3. **\( 2 + \pi \)**: This is an irrational number. The sum of a rational number (2) and an irrational number (\( \pi \)) is always irrational.

4. **\( 2 \cdot \pi \)**: This is also an irrational number. The product of a rational number (2) and an irrational number (\( \pi \)) is irrational.

### Final Classification:

- **Rational numbers**: 2
- **Irrational numbers**: \( \pi \), \( 2 + \pi \), \( 2 \cdot \pi \)

Would you like further details on any of these concepts?

Here are 5 questions to explore this topic further:
1. What are the key differences between rational and irrational numbers?
2. How can we prove that \( \pi \) is irrational?
3. Is the product of two irrational numbers always irrational?
4. Can irrational numbers be written as exact decimals?
5. Why do we consider sums involving irrational numbers irrational?

**Tip**: A rational number is any number that can be written as a simple fraction (ratio), while irrational numbers cannot be written this way.

Classify the numbers as rational or irrational: 2, π, 2 + π, 2 · π

Learn how to classify numbers as rational or irrational by analyzing 2, π, 2 + π, and 2 · π. Understand the difference between these number types and explore properties of sums and products of rational and irrational numbers. Suitable for students in Grades 7-9.

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