Sure, let's convert each improper fraction into a mixed number step-by-step.
### Part (a)
[tex]\[
\frac{13}{2}
\][/tex]
1. Perform the division of the numerator by the denominator:
[tex]\[
13 \div 2 = 6 \quad \text{remainder } 1
\][/tex]
2. Express this as a mixed number:
[tex]\[
13 = 6 \cdot 2 + 1 \implies \frac{13}{2} = 6 \frac{1}{2}
\][/tex]
So, [tex]\(\frac{13}{2} = 6 \frac{1}{2}\)[/tex].
### Part (b)
[tex]\[
\frac{19}{5}
\][/tex]
1. Perform the division of the numerator by the denominator:
[tex]\[
19 \div 5 = 3 \quad \text{remainder } 4
\][/tex]
2. Express this as a mixed number:
[tex]\[
19 = 3 \cdot 5 + 4 \implies \frac{19}{5} = 3 \frac{4}{5}
\][/tex]
So, [tex]\(\frac{19}{5} = 3 \frac{4}{5}\)[/tex].
### Part (c)
[tex]\[
\frac{41}{4}
\][/tex]
1. Perform the division of the numerator by the denominator:
[tex]\[
41 \div 4 = 10 \quad \text{remainder } 1
\][/tex]
2. Express this as a mixed number:
[tex]\[
41 = 10 \cdot 4 + 1 \implies \frac{41}{4} = 10 \frac{1}{4}
\][/tex]
So, [tex]\(\frac{41}{4} = 10 \frac{1}{4}\)[/tex].
Thus, the final mixed numbers are:
- [tex]\(\frac{13}{2} = 6 \frac{1}{2}\)[/tex]
- [tex]\(\frac{19}{5} = 3 \frac{4}{5}\)[/tex]
- [tex]\(\frac{41}{4} = 10 \frac{1}{4}\)[/tex]
