5.488 Найдите значение выражения: б) \frac{5}{12}b при b = \frac{1}{5}, b = \frac{5}{12}, b = \frac{6}{5}, b = \frac{84}{25}, b = 0.

б) Найдем значение выражения:

1. $$b = \frac{1}{5}$$

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

2. $$b = \frac{5}{12}$$

   $$\frac{5}{12}b = \frac{5}{12} \cdot \frac{5}{12} = \frac{5 \cdot 5}{12 \cdot 12} = \frac{25}{144}$$

3. $$b = \frac{6}{5}$$

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

4. $$b = \frac{84}{25}$$

   $$\frac{5}{12}b = \frac{5}{12} \cdot \frac{84}{25} = \frac{5 \cdot 84}{12 \cdot 25} = \frac{5 \cdot 12 \cdot 7}{12 \cdot 5 \cdot 5} = \frac{7}{5} = 1\frac{2}{5}$$

5. $$b = 0$$

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

Ответ: $$\frac{1}{12}; \frac{25}{144}; \frac{1}{2}; 1\frac{2}{5}; 0$$