State why we may conclude that each number below is rational. $$ \begin{array}{llll}\text { (1) } 1 \frac{3}{4} & \text { (2) }-3 \frac{1}{8} & \text { (3) } 4 & \text { (4) }-5 \ \text { (5) } 0,52 & \text { (6) } 1,212 & \end{array} $$

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A **rational number** is any number that can be expressed as the quotient or fraction $$\frac{a}{b}$$ of two integers, where $$b \neq 0$$. Let's analyze each number to see how it fits this definition:

1. **$$1 \frac{3}{4}$$**
   - **Explanation:** This is a mixed number, which can be converted to an improper fraction:
     $$
     1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}
     $$
   - **Conclusion:** Since it can be expressed as $$\frac{7}{4}$$, it is rational.

2. **$$-3 \frac{1}{8}$$**
   - **Explanation:** This mixed number can also be converted to an improper fraction:
     $$
     -3 \frac{1}{8} = -\left(\frac{8 \times 3 + 1}{8}\right) = -\frac{25}{8}
     $$
   - **Conclusion:** It is expressed as $$-\frac{25}{8}$$, making it rational.

3. **$$4$$**
   - **Explanation:** Any integer can be written as a fraction with denominator 1:
     $$
     4 = \frac{4}{1}
     $$
   - **Conclusion:** As $$\frac{4}{1}$$ is a ratio of integers, 4 is rational.

4. **$$-5$$**
   - **Explanation:** Similar to the previous integer:
     $$
     -5 = \frac{-5}{1}
     $$
   - **Conclusion:** $$\frac{-5}{1}$$ shows that -5 is rational.

5. **$$0.52$$**
   - **Explanation:** This is a finite decimal, which can be converted to a fraction:
     $$
     0.52 = \frac{52}{100} = \frac{13}{25}
     $$
   - **Conclusion:** Since it simplifies to $$\frac{13}{25}$$, 0.52 is rational.

6. **$$1.212$$**
   - **Explanation:** Another finite decimal that can be expressed as a fraction:
     $$
     1.212 = \frac{1212}{1000} = \frac{303}{250}
     $$
   - **Conclusion:** With $$\frac{303}{250}$$ as its fractional form, 1.212 is rational.

**Summary:**  
All the given numbers can be written as fractions where both the numerator and the denominator are integers (with the denominator not being zero). This satisfies the definition of rational numbers.

Answer: Because each can be written as a fraction of integers, for example:
 1 3⁄4 = 7⁄4;
 –3 1⁄8 = –25⁄8;
 4 = 4⁄1;
 –5 = –5⁄1;
 0.52 = 52⁄100;
 and 1.212 = 1212⁄1000.
Thus, all are rational numbers.
Each number can be expressed as a fraction of integers, so they are all rational.

State why we may conclude that each number below is rational.

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