1. Найдите значение выражения: a) 22/23 - 18/23 + 5/23; б) 8 7/9 + (7 5/9 - 4 4/9); в) 11 2/19 - (3 17/19 + 6 14/19).

Решение:

а)

• \[ \frac{22}{23} - \frac{18}{23} + \frac{5}{23} = \frac{22 - 18 + 5}{23} = \frac{4 + 5}{23} = \frac{9}{23} \]

б)

• \[ 8\frac{7}{9} + \left(7\frac{5}{9} - 4\frac{4}{9}\right) = 8\frac{7}{9} + \left((7-4) + \left(\frac{5}{9} - \frac{4}{9}\right)\right) = 8\frac{7}{9} + \left(3 + \frac{1}{9}\right) = 8\frac{7}{9} + 3\frac{1}{9} = (8+3) + \left(\frac{7}{9} + \frac{1}{9}\right) = 11 + \frac{8}{9} = 11\frac{8}{9} \]

в)

• \[ 11\frac{2}{19} - \left(3\frac{17}{19} + 6\frac{14}{19}\right) = 11\frac{2}{19} - \left((3+6) + \left(\frac{17}{19} + \frac{14}{19}\right)\right) = 11\frac{2}{19} - \left(9 + \frac{31}{19}\right) = 11\frac{2}{19} - \left(9 + 1\frac{12}{19}\right) = 11\frac{2}{19} - 10\frac{12}{19} \]
• \[ 11\frac{2}{19} - 10\frac{12}{19} = \frac{11 \times 19 + 2}{19} - \frac{10 \times 19 + 12}{19} = \frac{209 + 2}{19} - \frac{190 + 12}{19} = \frac{211}{19} - \frac{202}{19} = \frac{211 - 202}{19} = \frac{9}{19} \]

Ответ: а) 9/23; б) 11 8/9; в) 9/19.