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

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

UpStudy AI · Accepted Answer

To determine why each of the given numbers is **rational**, let's recall the definition:

**A rational number is any number that can be expressed as the ratio of two integers**, where the denominator is not zero. In other words, a number $$ r $$ is rational if it can be written in the form:
$$
r = \frac{a}{b}
$$
where $$ a $$ and $$ b $$ are integers, and $$ b \neq 0 $$.

Let's analyze each number:

1. **$$ 1 \frac{3}{4} $$**
   - **Conversion to an improper fraction:**
     $$
     1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}
     $$
   - **Conclusion:** It's expressed as $$ \frac{7}{4} $$, where both 7 and 4 are integers.

2. **$$ -3 \frac{1}{8} $$**
   - **Conversion to an improper fraction:**
     $$
     -3 \frac{1}{8} = -\left(\frac{8 \times 3 + 1}{8}\right) = -\frac{25}{8}
     $$
   - **Conclusion:** It's expressed as $$ -\frac{25}{8} $$, where both 25 and 8 are integers.

3. **$$ 4 $$**
   - **Expressed as a fraction:**
     $$
     4 = \frac{4}{1}
     $$
   - **Conclusion:** It's expressed as $$ \frac{4}{1} $$, where both 4 and 1 are integers.

5. **$$ 0.52 $$**
   - **Conversion to a fraction:**
     $$
     0.52 = \frac{52}{100} = \frac{13}{25} \quad (\text{after simplifying by dividing numerator and denominator by 4})
     $$
   - **Conclusion:** It's expressed as $$ \frac{13}{25} $$, where both 13 and 25 are integers.

6. **$$ 1.212 $$**
   - **Conversion to a fraction:**
     $$
     1.212 = \frac{1212}{1000} = \frac{303}{250} \quad (\text{after simplifying by dividing numerator and denominator by 4})
     $$
   - **Conclusion:** It's expressed as $$ \frac{303}{250} $$, where both 303 and 250 are integers.

**Summary:**  
Each number can be written as a fraction $$\frac{a}{b}$$ where $$ a $$ and $$ b $$ are integers and $$ b \neq 0 $$. Therefore, all the given numbers are **rational**.
Each number can be expressed as a fraction of two integers, so they are all rational.

© State why we maxy conelode that each number below is rational.

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