56. Преобразуйте десятичные дроби в обыкновенные и вычислите: 1) 0,2+\(\frac{1}{7}\); 2)\(\frac{7}{16}\)-0,12; 3) 4,85-2\(\frac{13}{24}\); 4)7\(\frac{8}{21}\)-4,375.

Решение:

1. \(0,2 + \frac{1}{7} = \frac{2}{10} + \frac{1}{7} = \frac{1}{5} + \frac{1}{7} = \frac{7}{35} + \frac{5}{35} = \frac{12}{35}\)
2. \(\frac{7}{16} - 0,12 = \frac{7}{16} - \frac{12}{100} = \frac{7}{16} - \frac{3}{25} = \frac{7 \cdot 25 - 3 \cdot 16}{16 \cdot 25} = \frac{175 - 48}{400} = \frac{127}{400}\)
3. \(4,85 - 2\frac{13}{24} = \frac{485}{100} - \frac{2 \cdot 24 + 13}{24} = \frac{97}{20} - \frac{48+13}{24} = \frac{97}{20} - \frac{61}{24} = \frac{97 \cdot 6 - 61 \cdot 5}{120} = \frac{582 - 305}{120} = \frac{277}{120} = 2\frac{37}{120}\)
4. \(7\frac{8}{21} - 4,375 = \frac{7 \cdot 21 + 8}{21} - \frac{4375}{1000} = \frac{147+8}{21} - \frac{35}{8} = \frac{155}{21} - \frac{35}{8} = \frac{155 \cdot 8 - 35 \cdot 21}{21 \cdot 8} = \frac{1240 - 735}{168} = \frac{505}{168} = 3\frac{1}{168}\)

Ответ: 1) \(\frac{12}{35}\); 2) \(\frac{127}{400}\); 3) \(2\frac{37}{120}\); 4) \(3\frac{1}{168}\).