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Let's go through each part of the Algebra assignment focusing on rational and irrational numbers.

### Part A: Identifying Rational and Irrational Numbers

1. **Circle the rational numbers in the list below:**
   - **\( \frac{1}{2} \)**: Rational (can be expressed as a fraction)
   - **\( \sqrt{3} \)**: Irrational (cannot be expressed as a simple fraction; its decimal expansion is non-repeating and infinite)
   - **0.25**: Rational (equivalent to \( \frac{1}{4} \))
   - **\( \pi \)**: Irrational (its decimal expansion is non-terminating and non-repeating)
   - **\( \frac{5}{3} \)**: Rational (can be expressed as a fraction)
   - **1.414...\** (assuming it refers to the square root of 2): Irrational (square root of 2 is known to be irrational)
   - **\( \sqrt{4} \)**: Rational (equal to 2, which can be expressed as \( \frac{2}{1} \))

   **Rational numbers circled**: \( \frac{1}{2} \), 0.25, \( \frac{5}{3} \), \( \sqrt{4} \).

2. **Write down whether the following numbers are rational or irrational:**
   - **\( \frac{7}{8} \)**: Rational
   - **\( \sqrt{5} \)**: Irrational
   - **2.75**: Rational (equivalent to \( \frac{11}{4} \))
   - **\( \frac{9}{2} \)**: Rational
   - **\( \pi \)**: Irrational

### Part B: Basic Understanding

3. **In your own words, define a rational number:**
   - **Definition**: A rational number is any number that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \neq 0 \). This includes all integers, finite decimals, and repeating decimals.

4. **In your own words, define an irrational number:**
   - **Definition**: An irrational number is a number that cannot be expressed as a simple fraction. Its decimal expansion is non-terminating and does not repeat. Examples include \( \pi \) and \( \sqrt{2} \).

If you need more details or have any questions, feel free to ask!

#### Questions to Consider:
1. Why is every integer considered a rational number?
2. How can you determine if a square root is rational or irrational without a calculator?
3. What is the difference between non-repeating decimals and repeating decimals?
4. Can an irrational number become rational by any mathematical operations?
5. Why is the number \( \pi \) so significant in mathematics beyond its classification as irrational?

#### Tip:
When examining whether a square root is rational or irrational, consider the properties of the number under the square root. If it's not a perfect square, the root is typically irrational.

Part A: Identifying Rational and Irrational Numbers. 1. Circle the rational numbers in the list below: 1/2, √3, 0.25, π, 5/3, 1.414..., √4. 2. Write down whether the following numbers are rational or irrational: 7/8, √5, 2.75, 9/2, π. Part B: Basic Understanding. 3. In your own words, define a rational number. 4. In your own words, define an irrational number.

Understand how to identify rational and irrational numbers with detailed examples. This includes working through problems like identifying whether numbers such as 1/2, √3, and π are rational or irrational, with step-by-step explanations for students in Grades 7-9.

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