Maligayang pagdating sa IDNStudy.com, ang iyong platform para sa lahat ng iyong katanungan! Ang aming komunidad ay handang magbigay ng malalim at maaasahang mga sagot, anuman ang kahirapan ng iyong mga katanungan.
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.