Answer :
Certainly! Let's solve the given problems step-by-step:
### Problem 1: \(\frac{p}{q} + \frac{r}{q}\)
1. Given: We have the fractions \(\frac{p}{q}\) and \(\frac{r}{q}\) where \(q \neq 0\).
2. Common Denominator: Notice that both fractions have the same denominator \(q\).
3. Addition: When adding fractions with the same denominator, we simply add the numerators together while keeping the denominator the same.
[tex]\[ \frac{p}{q} + \frac{r}{q} = \frac{p + r}{q} \][/tex]
Thus,
[tex]\[ \frac{p}{q} + \frac{r}{q} = \frac{p + r}{q} \][/tex]
### Problem 2: \(\frac{p}{q} - \frac{r}{q}\)
1. Given: Again, we have the fractions \(\frac{p}{q}\) and \(\frac{r}{q}\) where \(q \neq 0\).
2. Common Denominator: Notice that both fractions have the same denominator \(q\).
3. Subtraction: When subtracting fractions with the same denominator, we subtract the numerators while keeping the denominator the same.
[tex]\[ \frac{p}{q} - \frac{r}{q} = \frac{p - r}{q} \][/tex]
Thus,
[tex]\[ \frac{p}{q} - \frac{r}{q} = \frac{p - r}{q} \][/tex]
### Final Results
Putting it all together, we have:
1. \(\frac{p}{q} + \frac{r}{q} = \frac{p + r}{q}\)
2. \(\frac{p}{q} - \frac{r}{q} = \frac{p - r}{q}\)
These are the simplified forms of the given expressions.
### Problem 1: \(\frac{p}{q} + \frac{r}{q}\)
1. Given: We have the fractions \(\frac{p}{q}\) and \(\frac{r}{q}\) where \(q \neq 0\).
2. Common Denominator: Notice that both fractions have the same denominator \(q\).
3. Addition: When adding fractions with the same denominator, we simply add the numerators together while keeping the denominator the same.
[tex]\[ \frac{p}{q} + \frac{r}{q} = \frac{p + r}{q} \][/tex]
Thus,
[tex]\[ \frac{p}{q} + \frac{r}{q} = \frac{p + r}{q} \][/tex]
### Problem 2: \(\frac{p}{q} - \frac{r}{q}\)
1. Given: Again, we have the fractions \(\frac{p}{q}\) and \(\frac{r}{q}\) where \(q \neq 0\).
2. Common Denominator: Notice that both fractions have the same denominator \(q\).
3. Subtraction: When subtracting fractions with the same denominator, we subtract the numerators while keeping the denominator the same.
[tex]\[ \frac{p}{q} - \frac{r}{q} = \frac{p - r}{q} \][/tex]
Thus,
[tex]\[ \frac{p}{q} - \frac{r}{q} = \frac{p - r}{q} \][/tex]
### Final Results
Putting it all together, we have:
1. \(\frac{p}{q} + \frac{r}{q} = \frac{p + r}{q}\)
2. \(\frac{p}{q} - \frac{r}{q} = \frac{p - r}{q}\)
These are the simplified forms of the given expressions.
