Algebra 2 Worksheets | Basics for Algebra 2 Worksheets - Free Printable

Problem: Classify each number into the appropriate sets of real numbers.

The sets to consider are:
- ℕ (Natural Numbers): Positive integers starting from 1.
- 𝕎 (Whole Numbers): Non-negative integers (0, 1, 2, ...).
- ℤ (Integers): All whole numbers and their negatives.
- ℚ (Rational Numbers): Numbers that can be expressed as a ratio of two integers (\( \frac{p}{q} \), where \( q \neq 0 \)).
- ℝ (Real Numbers): All rational and irrational numbers.
- ℐ (Irrational Numbers): Numbers that cannot be expressed as a ratio of two integers.

Let's classify each number step by step:

---

#### 1) -46
- Classification:
- It is an integer because it is a whole number with a negative sign.
- It is a rational number because it can be written as \( \frac{-46}{1} \).
- It is a real number because all integers are real numbers.
- Sets: ℤ, ℚ, ℝ

#### 2) \( \frac{147}{7} \)
- Simplify: \( \frac{147}{7} = 21 \)
- Classification:
- It is a natural number because it is a positive integer.
- It is a whole number because it is a non-negative integer.
- It is an integer because it is a whole number.
- It is a rational number because it can be expressed as a fraction.
- It is a real number because all integers are real numbers.
- Sets: ℕ, 𝕎, ℤ, ℚ, ℝ

#### 3) 582
- Classification:
- It is a natural number because it is a positive integer.
- It is a whole number because it is a non-negative integer.
- It is an integer because it is a whole number.
- It is a rational number because it can be written as \( \frac{582}{1} \).
- It is a real number because all integers are real numbers.
- Sets: ℕ, 𝕎, ℤ, ℚ, ℝ

#### 4) \( \frac{23}{59} \)
- Classification:
- It is a rational number because it is expressed as a ratio of two integers.
- It is a real number because all rational numbers are real numbers.
- Sets: ℚ, ℝ

#### 5) \( \frac{56}{4} \)
- Simplify: \( \frac{56}{4} = 14 \)
- Classification:
- It is a natural number because it is a positive integer.
- It is a whole number because it is a non-negative integer.
- It is an integer because it is a whole number.
- It is a rational number because it can be expressed as a fraction.
- It is a real number because all integers are real numbers.
- Sets: ℕ, 𝕎, ℤ, ℚ, ℝ

#### 6) \( \sqrt{36} \)
- Simplify: \( \sqrt{36} = 6 \)
- Classification:
- It is a natural number because it is a positive integer.
- It is a whole number because it is a non-negative integer.
- It is an integer because it is a whole number.
- It is a rational number because it can be written as \( \frac{6}{1} \).
- It is a real number because all integers are real numbers.
- Sets: ℕ, 𝕎, ℤ, ℚ, ℝ

#### 7) \( \sqrt{51} \)
- Classification:
- It is an irrational number because \( \sqrt{51} \) cannot be expressed as a ratio of two integers.
- It is a real number because all irrational numbers are real numbers.
- Sets: ℐ, ℝ

#### 8) \( -\frac{48}{4} \)
- Simplify: \( -\frac{48}{4} = -12 \)
- Classification:
- It is an integer because it is a whole number with a negative sign.
- It is a rational number because it can be written as \( \frac{-12}{1} \).
- It is a real number because all integers are real numbers.
- Sets: ℤ, ℚ, ℝ

#### 9) π
- Classification:
- It is an irrational number because π cannot be expressed as a ratio of two integers.
- It is a real number because all irrational numbers are real numbers.
- Sets: ℐ, ℝ

#### 10) \( \sqrt{289} \)
- Simplify: \( \sqrt{289} = 17 \)
- Classification:
- It is a natural number because it is a positive integer.
- It is a whole number because it is a non-negative integer.
- It is an integer because it is a whole number.
- It is a rational number because it can be written as \( \frac{17}{1} \).
- It is a real number because all integers are real numbers.
- Sets: ℕ, 𝕎, ℤ, ℚ, ℝ

#### 11) -436
- Classification:
- It is an integer because it is a whole number with a negative sign.
- It is a rational number because it can be written as \( \frac{-436}{1} \).
- It is a real number because all integers are real numbers.
- Sets: ℤ, ℚ, ℝ

#### 12) \( \frac{17}{43} \)
- Classification:
- It is a rational number because it is expressed as a ratio of two integers.
- It is a real number because all rational numbers are real numbers.
- Sets: ℚ, ℝ

#### 13) 763
- Classification:
- It is a natural number because it is a positive integer.
- It is a whole number because it is a non-negative integer.
- It is an integer because it is a whole number.
- It is a rational number because it can be written as \( \frac{763}{1} \).
- It is a real number because all integers are real numbers.
- Sets: ℕ, 𝕎, ℤ, ℚ, ℝ

#### 14) 0
- Classification:
- It is a whole number because it is a non-negative integer.
- It is an integer because it is a whole number.
- It is a rational number because it can be written as \( \frac{0}{1} \).
- It is a real number because all integers are real numbers.
- Sets: 𝕎, ℤ, ℚ, ℝ

---

Final Answer:

\[
\boxed{
\begin{array}{ll}
1) & \text{Z, Q, R} \\
2) & \text{N, W, Z, Q, R} \\
3) & \text{N, W, Z, Q, R} \\
4) & \text{Q, R} \\
5) & \text{N, W, Z, Q, R} \\
6) & \text{N, W, Z, Q, R} \\
7) & \text{I, R} \\
8) & \text{Z, Q, R} \\
9) & \text{I, R} \\
10) & \text{N, W, Z, Q, R} \\
11) & \text{Z, Q, R} \\
12) & \text{Q, R} \\
13) & \text{N, W, Z, Q, R} \\
14) & \text{W, Z, Q, R} \\
\end{array}
}
\]