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 \(b = \frac{1}{5}\), \(b = \frac{5}{12}\), \(b = \frac{84}{25}\), \(b = 0\).

Краткое пояснение:

Пошаговое решение:

а) \(\frac{3}{7} a\)

• При \(a = \frac{119}{66}\): \(\frac{3}{7} \cdot \frac{119}{66} = \frac{3 \cdot 119}{7 \cdot 66} = \frac{1 \cdot 17}{1 \cdot 22} = \frac{17}{22}\)
• При \(a = \frac{28}{33}\): \(\frac{3}{7} \cdot \frac{28}{33} = \frac{3 \cdot 28}{7 \cdot 33} = \frac{1 \cdot 4}{1 \cdot 11} = \frac{4}{11}\)
• При \(a = 1\): \(\frac{3}{7} \cdot 1 = \frac{3}{7}\)

б) \(\frac{5}{12} b\)

• При \(b = \frac{1}{5}\): \(\frac{5}{12} \cdot \frac{1}{5} = \frac{5 \cdot 1}{12 \cdot 5} = \frac{1}{12}\)
• При \(b = \frac{5}{12}\): \(\frac{5}{12} \cdot \frac{5}{12} = \frac{25}{144}\)
• При \(b = \frac{84}{25}\): \(\frac{5}{12} \cdot \frac{84}{25} = \frac{5 \cdot 84}{12 \cdot 25} = \frac{1 \cdot 7}{1 \cdot 5} = \frac{7}{5} = 1\frac{2}{5}\)
• При \(b = 0\): \(\frac{5}{12} \cdot 0 = 0\)

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