Solve the following fraction addition problems: 1/3 + 2/7 5/7 + 1/4 5/6 + 7/11 1/3 + 7/10 2/5 + 3/7

Решение:

Для сложения дробей приведём их к общему знаменателю.

1. \( \frac{1}{3} + \frac{2}{7} = \frac{1 \cdot 7}{3 \cdot 7} + \frac{2 \cdot 3}{7 \cdot 3} = \frac{7}{21} + \frac{6}{21} = \frac{7+6}{21} = \frac{13}{21} \)
2. \( \frac{5}{7} + \frac{1}{4} = \frac{5 \cdot 4}{7 \cdot 4} + \frac{1 \cdot 7}{4 \cdot 7} = \frac{20}{28} + \frac{7}{28} = \frac{20+7}{28} = \frac{27}{28} \)
3. \( \frac{5}{6} + \frac{7}{11} = \frac{5 \cdot 11}{6 \cdot 11} + \frac{7 \cdot 6}{11 \cdot 6} = \frac{55}{66} + \frac{42}{66} = \frac{55+42}{66} = \frac{97}{66} \)
4. \( \frac{1}{3} + \frac{7}{10} = \frac{1 \cdot 10}{3 \cdot 10} + \frac{7 \cdot 3}{10 \cdot 3} = \frac{10}{30} + \frac{21}{30} = \frac{10+21}{30} = \frac{31}{30} \)
5. \( \frac{2}{5} + \frac{3}{7} = \frac{2 \cdot 7}{5 \cdot 7} + \frac{3 \cdot 5}{7 \cdot 5} = \frac{14}{35} + \frac{15}{35} = \frac{14+15}{35} = \frac{29}{35} \)

Ответ: \( \frac{13}{21}, \frac{27}{28}, \frac{97}{66}, \frac{31}{30}, \frac{29}{35} \).