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

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

1) при \(a = \frac{3}{7}\), \(\frac{3}{7} \cdot \frac{3}{7} = \frac{3 \cdot 3}{7 \cdot 7} = \frac{9}{49}\)

2) при \(a = \frac{119}{66}\), \(\frac{3}{7} \cdot \frac{119}{66} = \frac{3 \cdot 119}{7 \cdot 66} = \frac{3 \cdot 7 \cdot 17}{7 \cdot 6 \cdot 11} = \frac{3 \cdot 7 \cdot 17}{7 \cdot 2 \cdot 3 \cdot 11} = \frac{17}{22}\)

3) при \(a = \frac{28}{33}\), \(\frac{3}{7} \cdot \frac{28}{33} = \frac{3 \cdot 28}{7 \cdot 33} = \frac{3 \cdot 4 \cdot 7}{7 \cdot 3 \cdot 11} = \frac{4}{11}\)

4) при \(a = 1\), \(\frac{3}{7} \cdot 1 = \frac{3}{7}\)

Ответ: 1) \(\frac{9}{49}\); 2) \(\frac{17}{22}\); 3) \(\frac{4}{11}\); 4) \(\frac{3}{7}\)

б) \(\frac{5}{12}b\)

1) при \(b = \frac{1}{5}\), \(\frac{5}{12} \cdot \frac{1}{5} = \frac{5 \cdot 1}{12 \cdot 5} = \frac{1}{12}\)

2) при \(b = \frac{5}{12}\), \(\frac{5}{12} \cdot \frac{5}{12} = \frac{5 \cdot 5}{12 \cdot 12} = \frac{25}{144}\)

3) при \(b = \frac{6}{5}\), \(\frac{5}{12} \cdot \frac{6}{5} = \frac{5 \cdot 6}{12 \cdot 5} = \frac{6}{12} = \frac{1}{2}\)

4) при \(b = \frac{84}{25}\), \(\frac{5}{12} \cdot \frac{84}{25} = \frac{5 \cdot 84}{12 \cdot 25} = \frac{5 \cdot 12 \cdot 7}{12 \cdot 5 \cdot 5} = \frac{7}{5} = 1\frac{2}{5}\)

5) при \(b = 0\), \(\frac{5}{12} \cdot 0 = 0\)

Ответ: 1) \(\frac{1}{12}\); 2) \(\frac{25}{144}\); 3) \(\frac{1}{2}\); 4) \(1\frac{2}{5}\); 5) \(0\)