5.419 Найдите сумму c/10 + c/25 при c = 1; c = 3; c = 7; c = 9.

Найдем сумму c/10 + c/25 при с = 1, с = 3, с = 7, с = 9.

1) При с = 1:

$$\frac{c}{10} + \frac{c}{25} = \frac{1}{10} + \frac{1}{25} = \frac{1 \cdot 5}{10 \cdot 5} + \frac{1 \cdot 2}{25 \cdot 2} = \frac{5}{50} + \frac{2}{50} = \frac{5+2}{50} = \frac{7}{50}$$

2) При с = 3:

$$\frac{c}{10} + \frac{c}{25} = \frac{3}{10} + \frac{3}{25} = \frac{3 \cdot 5}{10 \cdot 5} + \frac{3 \cdot 2}{25 \cdot 2} = \frac{15}{50} + \frac{6}{50} = \frac{15+6}{50} = \frac{21}{50}$$

3) При с = 7:

$$\frac{c}{10} + \frac{c}{25} = \frac{7}{10} + \frac{7}{25} = \frac{7 \cdot 5}{10 \cdot 5} + \frac{7 \cdot 2}{25 \cdot 2} = \frac{35}{50} + \frac{14}{50} = \frac{35+14}{50} = \frac{49}{50}$$

4) При с = 9:

$$\frac{c}{10} + \frac{c}{25} = \frac{9}{10} + \frac{9}{25} = \frac{9 \cdot 5}{10 \cdot 5} + \frac{9 \cdot 2}{25 \cdot 2} = \frac{45}{50} + \frac{18}{50} = \frac{45+18}{50} = \frac{63}{50} = 1\frac{13}{50}$$

Ответ: 7/50; 21/50; 49/50; 1 13/50