№1. Выполните действия: a) 20 \frac{17}{37}+14\frac{12}{37}+31\frac{8}{37}; б) 6 \frac{100}{107}+9\frac{106}{107}; в) 12\frac{19}{32}-4\frac{3}{32}; г) 150-\frac{149}{150}; д) 17\frac{2}{13}-16\frac{5}{13}.

a) $$20 \frac{17}{37}+14\frac{12}{37}+31\frac{8}{37} = (20+14+31) + (\frac{17}{37}+\frac{12}{37}+\frac{8}{37}) = 65 + \frac{17+12+8}{37} = 65 + \frac{37}{37} = 65 + 1 = 66$$

Ответ: 66

б) $$6 \frac{100}{107}+9\frac{106}{107} = (6+9) + (\frac{100}{107}+\frac{106}{107}) = 15 + \frac{100+106}{107} = 15 + \frac{206}{107} = 15 + 1\frac{99}{107} = 16\frac{99}{107}$$

Ответ: $$16\frac{99}{107}$$

в) $$12\frac{19}{32}-4\frac{3}{32} = (12-4) + (\frac{19}{32}-\frac{3}{32}) = 8 + \frac{19-3}{32} = 8 + \frac{16}{32} = 8 + \frac{1}{2} = 8\frac{1}{2}$$

Ответ: $$8\frac{1}{2}$$

г) $$150-\frac{149}{150} = 149 + 1 - \frac{149}{150} = 149 + \frac{150}{150} - \frac{149}{150} = 149 + \frac{150-149}{150} = 149 + \frac{1}{150} = 149\frac{1}{150}$$

Ответ: $$149\frac{1}{150}$$

д) $$17\frac{2}{13}-16\frac{5}{13} = (17-16) + (\frac{2}{13}-\frac{5}{13}) = 1 + \frac{2-5}{13} = 1 - \frac{3}{13} = \frac{13}{13} - \frac{3}{13} = \frac{13-3}{13} = \frac{10}{13}$$

Ответ: $$\frac{10}{13}$$