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Name: [tex]$\qquad$[/tex]
[tex]$\qquad$[/tex] Unit 1: Algebra Basics

Date: [tex]$\qquad$[/tex] Bell: [tex]$\qquad$[/tex] Homework 1: The Real Numbers

Directions: Name all sets of numbers to which each real number belongs.

1. 12
2. -15
3. [tex]$1 \frac{1}{2}$[/tex]
4. [tex]$3.18 - \operatorname{rat}, R$[/tex]
5. [tex]$\sqrt{48}$[/tex]
6. [tex]$9 \overline{3} - \operatorname{rat}, R$[/tex]
7. [tex]$-2 \frac{7}{9}$[/tex]
8. [tex]$\sqrt{25} = 5 - N_1 W_1 I, \operatorname{rat}, R$[/tex]
9. [tex]$\sqrt{3}$[/tex]
10. [tex]$-\sqrt{64}$[/tex]
11. [tex]$-\sqrt{12}$[/tex]
12. [tex]$\frac{8}{4}$[/tex]

Directions: Place the LETTER of each value in its location in the real number system below.

A. 2.125
B. 0
C. Rational

[tex]$A: F$[/tex]



Answer :

GinnyAnswer
Alright, the task is to correctly identify the sets of numbers each given number belongs to. Let's go through each number step-by-step:

1. 12
- 12 is a positive whole number.
- It belongs to the set of natural numbers (N).
- It belongs to the set of whole numbers (W).
- It belongs to the set of integers (Z).
- It belongs to the set of rational numbers (Q).
- It belongs to the set of real numbers (R).

So, 12 belongs to [tex]\(N, W, Z, Q, R\)[/tex].

2. -15
- -15 is a negative whole number.
- It belongs to the set of integers (Z).
- It belongs to the set of rational numbers (Q).
- It belongs to the set of real numbers (R).

So, -15 belongs to [tex]\(Z, Q, R\)[/tex].

3. [tex]\(1 \frac{1}{2}\)[/tex]
- [tex]\(1 \frac{1}{2}\)[/tex] or 1.5 is a positive fraction.
- It belongs to the set of rational numbers (Q).
- It belongs to the set of real numbers (R).

So, [tex]\(1 \frac{1}{2}\)[/tex] belongs to [tex]\(Q, R\)[/tex].

4. 3.18
- 3.18 is a decimal number.
- It belongs to the set of rational numbers (Q).
- It belongs to the set of real numbers (R).

So, 3.18 belongs to [tex]\(Q, R\)[/tex].

5. [tex]\(\sqrt{48}\)[/tex]
- [tex]\(\sqrt{48}\)[/tex] is an irrational number.
- It belongs to the set of irrational numbers (I).
- It belongs to the set of real numbers (R).

So, [tex]\(\sqrt{48}\)[/tex] belongs to [tex]\(I, R\)[/tex].

6. 9.333... (recurring)
- 9.333… is a repeating decimal.
- It belongs to the set of rational numbers (Q).
- It belongs to the set of real numbers (R).

So, 9.333... belongs to [tex]\(Q, R\)[/tex].

7. [tex]\(-2 \frac{7}{9}\)[/tex]
- [tex]\(-2 \frac{7}{9}\)[/tex] is a negative fraction.
- It belongs to the set of rational numbers (Q).
- It belongs to the set of real numbers (R).

So, [tex]\(-2 \frac{7}{9}\)[/tex] belongs to [tex]\(Q, R\)[/tex].

8. [tex]\(\sqrt{25} = 5\)[/tex]
- [tex]\(\sqrt{25}\)[/tex] is a positive whole number.
- 5 is a positive whole number.
- It belongs to the set of natural numbers (N).
- It belongs to the set of whole numbers (W).
- It belongs to the set of integers (Z).
- It belongs to the set of rational numbers (Q).
- It belongs to the set of real numbers (R).

So, [tex]\(\sqrt{25} = 5\)[/tex] belongs to [tex]\(N, W, Z, Q, R\)[/tex].

9. [tex]\(\sqrt{3}\)[/tex]
- [tex]\(\sqrt{3}\)[/tex] is an irrational number.
- It belongs to the set of irrational numbers (I).
- It belongs to the set of real numbers (R).

So, [tex]\(\sqrt{3}\)[/tex] belongs to [tex]\(I, R\)[/tex].

10. [tex]\(-\sqrt{64} = -8\)[/tex]
- [tex]\(-\sqrt{64}\)[/tex] is a negative whole number.
- It belongs to the set of integers (Z).
- It belongs to the set of rational numbers (Q).
- It belongs to the set of real numbers (R).

So, [tex]\(-\sqrt{64} = -8\)[/tex] belongs to [tex]\(Z, Q, R\)[/tex].

11. [tex]\(-\sqrt{12}\)[/tex]
- [tex]\(-\sqrt{12}\)[/tex] is an irrational number.
- It belongs to the set of irrational numbers (I).
- It belongs to the set of real numbers (R).

So, [tex]\(-\sqrt{12}\)[/tex] belongs to [tex]\(I, R\)[/tex].

12. [tex]\(\frac{8}{4} = 2\)[/tex]
- [tex]\(\frac{8}{4}\)[/tex] simplifies to 2, a positive whole number.
- It belongs to the set of natural numbers (N).
- It belongs to the set of whole numbers (W).
- It belongs to the set of integers (Z).
- It belongs to the set of rational numbers (Q).
- It belongs to the set of real numbers (R).

So, [tex]\(\frac{8}{4} = 2\)[/tex] belongs to [tex]\(N, W, Z, Q, R\)[/tex].

Here is the complete set of answers:
1. 12 belongs to [tex]\(N, W, Z, Q, R\)[/tex].
2. -15 belongs to [tex]\(Z, Q, R\)[/tex].
3. [tex]\(1 \frac{1}{2}\)[/tex] belongs to [tex]\(Q, R\)[/tex].
4. 3.18 belongs to [tex]\(Q, R\)[/tex].
5. [tex]\(\sqrt{48}\)[/tex] belongs to [tex]\(I, R\)[/tex].
6. 9.333... (recurring) belongs to [tex]\(Q, R\)[/tex].
7. [tex]\(-2 \frac{7}{9}\)[/tex] belongs to [tex]\(Q, R\)[/tex].
8. [tex]\(\sqrt{25} = 5\)[/tex] belongs to [tex]\(N, W, Z, Q, R\)[/tex].
9. [tex]\(\sqrt{3}\)[/tex] belongs to [tex]\(I, R\)[/tex].
10. [tex]\(-\sqrt{64} = -8\)[/tex] belongs to [tex]\(Z, Q, R\)[/tex].
11. [tex]\(-\sqrt{12}\)[/tex] belongs to [tex]\(I, R\)[/tex].
12. [tex]\(\frac{8}{4} = 2\)[/tex] belongs to [tex]\(N, W, Z, Q, R\)[/tex].