Сумма и разность дробей с разными знаменателями

Пример:

\( \frac{7}{12} + \frac{2}{15} = \frac{7 \cdot 5}{12 \cdot 5} + \frac{2 \cdot 4}{15 \cdot 4} = \frac{35}{60} + \frac{8}{60} = \frac{35+8}{60} = \frac{43}{60} \)

Решение:

Задание 1:

1. \( \frac{6}{11} : 4 = \frac{6}{11 \cdot 4} = \frac{6}{44} \)
2. \( \frac{6}{7} : 6 = \frac{6}{7 \cdot 6} = \frac{1}{7} \)
3. \( \frac{6}{7} : 7 = \frac{6}{7 \cdot 7} = \frac{6}{49} \)
4. \( \frac{6}{13} : 3 = \frac{6}{13 \cdot 3} = \frac{2}{13} \)
5. \( \frac{8}{12} : 12 = \frac{8}{12 \cdot 12} = \frac{8}{144} = \frac{1}{18} \)
6. \( \frac{7}{9} : 9 = \frac{7}{9 \cdot 9} = \frac{7}{81} \)

Задание 2:

1. \( \frac{1}{40} : 30 = \frac{1}{40 \cdot 30} = \frac{1}{1200} \)
2. \( \frac{1}{49} : 50 = \frac{1}{49 \cdot 50} = \frac{1}{2450} \)
3. \( \frac{1}{13} : 3 = \frac{1}{13 \cdot 3} = \frac{1}{39} \)
4. \( \frac{15}{39} : 5 = \frac{15}{39 \cdot 5} = \frac{3}{39} = \frac{1}{13} \)
5. \( \frac{12}{6} : 6 = \frac{12}{6 \cdot 6} = \frac{12}{36} = \frac{1}{3} \)
6. \( \frac{8}{7} : 2 = \frac{8}{7 \cdot 2} = \frac{8}{14} = \frac{4}{7} \)

Задание 3:

Образец:

• \( \frac{1}{9} - \frac{2}{9} = -\frac{1}{9} \)
• \( \frac{2}{3} - \frac{3}{9} = \frac{2 \cdot 3}{3 \cdot 3} - \frac{3}{9} = \frac{6}{9} - \frac{3}{9} = \frac{3}{9} = \frac{1}{3} \)
• \( \frac{3}{9} - \frac{2}{9} = \frac{1}{9} \)
• \( \frac{3-2}{9} = \frac{1}{9} \)