100. Выполните действия: a) (1+23): 1+(1-):; 6) 6-1-2: 1+. 142. Решите уравнение: a) y = 1; 6) 12+7=10; 2) (+)= 3;

100. Выполните действия:

a) $$\left(1 \frac{3}{5} + 2 \frac{1}{2}\right) : 1 \frac{9}{10} + \left(1 \frac{7}{10} - \frac{4}{5}\right) : \frac{3}{7}$$;

1) $$1 \frac{3}{5} + 2 \frac{1}{2} = \frac{8}{5} + \frac{5}{2} = \frac{8 \cdot 2 + 5 \cdot 5}{10} = \frac{16+25}{10} = \frac{41}{10}$$;

2) $$1 \frac{9}{10} = \frac{19}{10}$$;

3) $$\frac{41}{10} : \frac{19}{10} = \frac{41}{10} \cdot \frac{10}{19} = \frac{41}{19} = 2 \frac{3}{19}$$;

4) $$1 \frac{7}{10} - \frac{4}{5} = \frac{17}{10} - \frac{4}{5} = \frac{17 - 4 \cdot 2}{10} = \frac{17-8}{10} = \frac{9}{10}$$;

5) $$\frac{9}{10} : \frac{3}{7} = \frac{9}{10} \cdot \frac{7}{3} = \frac{3 \cdot 7}{10} = \frac{21}{10} = 2 \frac{1}{10}$$;

6) $$2 \frac{3}{19} + 2 \frac{1}{10} = 2 + 2 + \frac{3}{19} + \frac{1}{10} = 4 + \frac{3 \cdot 10 + 1 \cdot 19}{190} = 4 + \frac{30+19}{190} = 4 + \frac{49}{190} = 4 \frac{49}{190}$$.

Ответ: $$4 \frac{49}{190}$$.

б) $$6 \frac{1}{8} : 1 \frac{7}{17} - 2 \frac{3}{8} : 1 \frac{1}{4} + \frac{2}{5}$$;

1) $$6 \frac{1}{8} : 1 \frac{7}{17} = \frac{49}{8} : \frac{24}{17} = \frac{49}{8} \cdot \frac{17}{24} = \frac{833}{192}$$;

2) $$2 \frac{3}{8} : 1 \frac{1}{4} = \frac{19}{8} : \frac{5}{4} = \frac{19}{8} \cdot \frac{4}{5} = \frac{19}{2 \cdot 5} = \frac{19}{10}$$;

3) $$\frac{833}{192} - \frac{19}{10} = \frac{833 \cdot 5 - 19 \cdot 96}{960} = \frac{4165 - 1824}{960} = \frac{2341}{960} = 2 \frac{421}{960}$$;

4) $$2 \frac{421}{960} + \frac{2}{5} = 2 + \frac{421}{960} + \frac{2}{5} = 2 + \frac{421 + 2 \cdot 192}{960} = 2 + \frac{421+384}{960} = 2 + \frac{805}{960} = 2 \frac{161}{192}$$.

Ответ: $$2 \frac{161}{192}$$.

142. Решите уравнение:

a) $$\frac{7}{8} y = 1 \frac{1}{4}$$;

$$\frac{7}{8} y = \frac{5}{4}$$;

$$y = \frac{5}{4} : \frac{7}{8}$$;

$$y = \frac{5}{4} \cdot \frac{8}{7} = \frac{5 \cdot 2}{7} = \frac{10}{7} = 1 \frac{3}{7}$$.

Ответ: $$y = 1 \frac{3}{7}$$.

б) $$\frac{1}{6} z + \frac{3}{7} = \frac{13}{8}$$;

$$\frac{1}{6} z = \frac{13}{8} - \frac{3}{7}$$;

$$\frac{1}{6} z = \frac{13 \cdot 7 - 3 \cdot 8}{56} = \frac{91-24}{56} = \frac{67}{56}$$;

$$z = \frac{67}{56} : \frac{1}{6}$$;

$$z = \frac{67 \cdot 6}{56} = \frac{67 \cdot 3}{28} = \frac{201}{28} = 7 \frac{5}{28}$$.

Ответ: $$z = 7 \frac{5}{28}$$.

г) $$\left(\frac{3}{14} + \frac{5}{21} x \right) : \frac{3}{7} = 3 \frac{1}{4}$$;

$$\left(\frac{3}{14} + \frac{5}{21} x \right) : \frac{3}{7} = \frac{13}{4}$$;

$$\frac{3}{14} + \frac{5}{21} x = \frac{13}{4} \cdot \frac{3}{7} = \frac{39}{28}$$;

$$\frac{5}{21} x = \frac{39}{28} - \frac{3}{14} = \frac{39 - 3 \cdot 2}{28} = \frac{39-6}{28} = \frac{33}{28}$$;

$$x = \frac{33}{28} : \frac{5}{21} = \frac{33 \cdot 21}{28 \cdot 5} = \frac{33 \cdot 3}{4 \cdot 5} = \frac{99}{20} = 4 \frac{19}{20}$$.

Ответ: $$x = 4 \frac{19}{20}$$.