5.488 Найдите значение выражения: а) \(\frac{3}{7}\)a при a = \(\frac{3}{7}\), a = \(\frac{119}{66}\), a = \(\frac{28}{33}\), a = 1; б) \(\frac{5}{12}\)b при b = \(\frac{1}{5}\), b = \(\frac{5}{12}\), b = \(\frac{6}{5}\), b = \(\frac{84}{25}\), b = 0.

**Решение:**

**a) \(\frac{3}{7}\)a**

1. **a = \(\frac{3}{7}\)**

\(\frac{3}{7}\) \(\cdot\) \(\frac{3}{7}\) = \(\frac{9}{49}\)
2. **a = \(\frac{119}{66}\)**

\(\frac{3}{7}\) \(\cdot\) \(\frac{119}{66}\) = \(\frac{3 \cdot 119}{7 \cdot 66}\) = \(\frac{357}{462}\) = \(\frac{17 \cdot 21}{22 \cdot 21}\) = \(\frac{17}{22}\)
3. **a = \(\frac{28}{33}\)**

\(\frac{3}{7}\) \(\cdot\) \(\frac{28}{33}\) = \(\frac{3 \cdot 28}{7 \cdot 33}\) = \(\frac{84}{231}\) = \(\frac{12 \cdot 7}{33 \cdot 7}\) = \(\frac{12}{33}\) = \(\frac{4 \cdot 3}{11 \cdot 3}\) = \(\frac{4}{11}\)
4. **a = 1**

\(\frac{3}{7}\) \(\cdot\) 1 = \(\frac{3}{7}\)

**б) \(\frac{5}{12}\)b**

1. **b = \(\frac{1}{5}\)**

\(\frac{5}{12}\) \(\cdot\) \(\frac{1}{5}\) = \(\frac{5}{60}\) = \(\frac{1}{12}\)
2. **b = \(\frac{5}{12}\)**

\(\frac{5}{12}\) \(\cdot\) \(\frac{5}{12}\) = \(\frac{25}{144}\)
3. **b = \(\frac{6}{5}\)**

\(\frac{5}{12}\) \(\cdot\) \(\frac{6}{5}\) = \(\frac{30}{60}\) = \(\frac{1}{2}\)
4. **b = \(\frac{84}{25}\)**

\(\frac{5}{12}\) \(\cdot\) \(\frac{84}{25}\) = \(\frac{420}{300}\) = \(\frac{42}{30}\) = \(\frac{7}{5}\)
5. **b = 0**

\(\frac{5}{12}\) \(\cdot\) 0 = 0

**Ответ:** a) \(\frac{9}{49}\), \(\frac{17}{22}\), \(\frac{4}{11}\), \(\frac{3}{7}\); б) \(\frac{1}{12}\), \(\frac{25}{144}\), \(\frac{1}{2}\), \(\frac{7}{5}\), 0