5.486 Найдите произведение: а) \(\frac{8}{9}\) \(\cdot\) \(\frac{3}{4}\); б) \(\frac{11}{45}\) \(\cdot\) \(\frac{9}{22}\); в) \(\frac{51}{29}\) \(\cdot\) \(\frac{58}{85}\); г) \(\frac{1}{4}\) \(\cdot\) \(\frac{4}{5}\) \(\cdot\) \(\frac{5}{6}\).

**Решение:**

**a) \(\frac{8}{9}\) \(\cdot\) \(\frac{3}{4}\)**

1. Умножим числители и знаменатели:

\(\frac{8 \cdot 3}{9 \cdot 4}\) = \(\frac{24}{36}\)
2. Сократим дробь на 12:

\(\frac{24:12}{36:12}\) = \(\frac{2}{3}\)

**б) \(\frac{11}{45}\) \(\cdot\) \(\frac{9}{22}\)**

1. Умножим числители и знаменатели:

\(\frac{11 \cdot 9}{45 \cdot 22}\) = \(\frac{99}{990}\)
2. Сократим дробь на 99:

\(\frac{99:99}{990:99}\) = \(\frac{1}{10}\)

**в) \(\frac{51}{29}\) \(\cdot\) \(\frac{58}{85}\)**

1. Умножим числители и знаменатели:

\(\frac{51 \cdot 58}{29 \cdot 85}\) = \(\frac{2958}{2465}\)
2. Сократим дробь на 17:

\(\frac{2958:17}{2465:17}\) = \(\frac{174}{145}\)
3. Сократим дробь на 29:

\(\frac{174:29}{145:29}\) = \(\frac{6}{5}\)

**г) \(\frac{1}{4}\) \(\cdot\) \(\frac{4}{5}\) \(\cdot\) \(\frac{5}{6}\)**

1. Умножим числители и знаменатели:

\(\frac{1 \cdot 4 \cdot 5}{4 \cdot 5 \cdot 6}\) = \(\frac{20}{120}\)
2. Сократим дробь на 20:

\(\frac{20:20}{120:20}\) = \(\frac{1}{6}\)

**Ответ:** а) \(\frac{2}{3}\); б) \(\frac{1}{10}\); в) \(\frac{6}{5}\); г) \(\frac{1}{6}\)