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Answer:
### A. Adding Fractions
To add fractions, we need a common denominator for each pair of fractions. Then we add the numerators and keep the denominator the same.
1. **\( \frac{1}{2} + \frac{5}{9} \)**
- Find the least common denominator (LCD) of 2 and 9, which is 18.
- Convert each fraction:
\[
\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}
\]
\[
\frac{5}{9} = \frac{5 \times 2}{9 \times 2} = \frac{10}{18}
\]
- Add the fractions:
\[
\frac{9}{18} + \frac{10}{18} = \frac{19}{18}
\]
- Since \(\frac{19}{18}\) is an improper fraction, convert it to a mixed number:
\[
\frac{19}{18} = 1 \frac{1}{18}
\]
2. **\( \frac{2}{4} + \frac{3}{8} \)**
- Simplify \(\frac{2}{4}\) to \(\frac{1}{2}\).
- Find the LCD of 2 and 8, which is 8.
- Convert each fraction:
\[
\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
\]
- Add the fractions:
\[
\frac{4}{8} + \frac{3}{8} = \frac{7}{8}
\]
3. **\( \frac{2}{6} + \frac{1}{5} \)**
- Simplify \(\frac{2}{6}\) to \(\frac{1}{3}\).
- Find the LCD of 3 and 5, which is 15.
- Convert each fraction:
\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]
\[
\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}
\]
- Add the fractions:
\[
\frac{5}{15} + \frac{3}{15} = \frac{8}{15}
\]
### B. Solving Word Problems
4. **Analie's Work Hours**
Analie worked for \(\frac{2}{7}\) hour on Saturday and \(\frac{3}{7}\) hour on Sunday.
- Both fractions have the same denominator, so add them directly:
\[
\frac{2}{7} + \frac{3}{7} = \frac{5}{7}
\]
- Analie worked \(\frac{5}{7}\) hours in total.
5. **Angelica's Total Cloth Cut**
Angelica cut \(\frac{2}{5}\) meter of green cloth, \(\frac{1}{4}\) meter of white cloth, and \(\frac{2}{8}\) meter of pink cloth.
- Simplify \(\frac{2}{8}\) to \(\frac{1}{4}\).
- Find the LCD of 5 and 4, which is 20.
- Convert each fraction:
\[
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}
\]
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]
- Add the fractions:
\[
\frac{8}{20} + \frac{5}{20} + \frac{5}{20} = \frac{18}{20}
\]
- Simplify \(\frac{18}{20}\) to \(\frac{9}{10}\).
- Angelica cut a total of \(\frac{9}{10}\) meter of cloth.