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

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**.