Let's break down each part of the question and provide detailed, step-by-step solutions.
1. Compute [tex]\(\frac{2}{8}\)[/tex]:
[tex]\[
\frac{2}{8} = 0.25
\][/tex]
2. Compute [tex]\(\frac{\frac{1}{3}}{14}\)[/tex]:
[tex]\[
\frac{\frac{1}{3}}{14} = \frac{1}{3 \times 14} = \frac{1}{42} \approx 0.02381
\][/tex]
3. Compute [tex]\(\frac{5}{11}\)[/tex]:
[tex]\[
\frac{5}{11} \approx 0.45455
\][/tex]
4. Compute [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
5. Compute [tex]\(\frac{\frac{1}{4}}{21}\)[/tex]:
[tex]\[
\frac{\frac{1}{4}}{21} = \frac{1}{4 \times 21} = \frac{1}{84} \approx 0.0119
\][/tex]
6. Compute [tex]\(\frac{\frac{3}{8}}{14}\)[/tex]:
[tex]\[
\frac{\frac{3}{8}}{14} = \frac{3}{8 \times 14} = \frac{3}{112} \approx 0.02679
\][/tex]
7. Compute [tex]\(\frac{4}{7} + \frac{2}{5}\)[/tex]:
- First, we need a common denominator:
[tex]\[
\frac{4}{7} = \frac{4 \times 5}{7 \times 5} = \frac{20}{35}
\][/tex]
[tex]\[
\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}
\][/tex]
- Now add them together:
[tex]\[
\frac{20}{35} + \frac{14}{35} = \frac{34}{35} \approx 0.97143
\][/tex]
8. Compute [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{1}{4} = 0.25
\][/tex]
9. Compute [tex]\(\frac{\frac{3}{5}}{13}\)[/tex]:
[tex]\[
\frac{\frac{3}{5}}{13} = \frac{3}{5 \times 13} = \frac{3}{65} \approx 0.04615
\][/tex]
These are the detailed solutions for each part of the given question.
