Let's solve the given problem step-by-step.
1. Simplify the first fraction:
[tex]\[
\frac{2}{8}
\][/tex]
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2.
[tex]\[
\frac{2 \div 2}{8 \div 2} = \frac{1}{4}
\][/tex]
So,
[tex]\[
\frac{2}{8} = \frac{1}{4} = 0.25
\][/tex]
2. Convert the fractions to a common denominator for addition:
To add [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex], we need a common denominator. The least common multiple of 4 and 5 is 20.
- Convert [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\][/tex]
- Convert [tex]\(\frac{4}{5}\)[/tex]:
[tex]\[
\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}
\][/tex]
3. Add the fractions:
Now, add [tex]\(\frac{5}{20}\)[/tex] and [tex]\(\frac{16}{20}\)[/tex]:
[tex]\[
\frac{5}{20} + \frac{16}{20} = \frac{5 + 16}{20} = \frac{21}{20}
\][/tex]
4. Convert the improper fraction to a decimal:
[tex]\[
\frac{21}{20} = 1.05
\][/tex]
Therefore, the simplified result of the first fraction is [tex]\(0.25\)[/tex] and the sum of the two fractions is [tex]\(1.05\)[/tex].
[tex]\[
\boxed{0.25 \quad \text{and} \quad 1.05}
\][/tex]
