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

а) \(\frac{3}{7}a\)

1. \(a = \frac{119}{66}\)

$$\frac{3}{7} \cdot \frac{119}{66} = \frac{3 \cdot 119}{7 \cdot 66} = \frac{357}{462} = \frac{17 \cdot 21}{22 \cdot 21} = \frac{17}{22}$$

2. \(a = \frac{28}{33}\)

$$\frac{3}{7} \cdot \frac{28}{33} = \frac{3 \cdot 28}{7 \cdot 33} = \frac{84}{231} = \frac{12 \cdot 7}{33 \cdot 7} = \frac{12}{33} = \frac{4 \cdot 3}{11 \cdot 3} = \frac{4}{11} $$

3. \(a = 1\)

$$\frac{3}{7} \cdot 1 = \frac{3}{7}$$

б) \(\frac{5}{12}b\)

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

$$\frac{5}{12} \cdot \frac{1}{5} = \frac{5 \cdot 1}{12 \cdot 5} = \frac{5}{60} = \frac{1}{12}$$

2. \(b = \frac{6}{5}\)

$$\frac{5}{12} \cdot \frac{6}{5} = \frac{5 \cdot 6}{12 \cdot 5} = \frac{30}{60} = \frac{1}{2}$$

3. \(b = \frac{84}{25}\)

$$\frac{5}{12} \cdot \frac{84}{25} = \frac{5 \cdot 84}{12 \cdot 25} = \frac{420}{300} = \frac{42}{30} = \frac{21}{15} = \frac{7}{5} = 1\frac{2}{5} $$

4. \(b = 0\)

$$\frac{5}{12} \cdot 0 = 0$$

Ответ: а) \(\frac{17}{22}\), \(\frac{4}{11}\), \(\frac{3}{7}\); б) \(\frac{1}{12}\), \(\frac{1}{2}\), \(1\frac{2}{5}\), \(0\)