To solve [tex]\(4 \frac{1}{2} \div 2 \frac{1}{2}\)[/tex], we can follow these steps:
1. Convert the mixed fractions to improper fractions:
- For [tex]\(4 \frac{1}{2}\)[/tex]:
[tex]\[
4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2}
\][/tex]
- For [tex]\(2 \frac{1}{2}\)[/tex]:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\][/tex]
2. Perform the division of the improper fractions:
To divide fractions, multiply by the reciprocal of the divisor.
[tex]\[
\frac{9}{2} \div \frac{5}{2} = \frac{9}{2} \times \frac{2}{5} = \frac{9 \times 2}{2 \times 5} = \frac{18}{10} = \frac{9}{5}
\][/tex]
3. Convert the result to a mixed fraction:
[tex]\[
\frac{9}{5} = 1 \frac{4}{5}
\][/tex]
So, [tex]\(4 \frac{1}{2} \div 2 \frac{1}{2} = 1 \frac{4}{5}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{D. \, 1 \frac{4}{5}}
\][/tex]
