Давай разберем примеры. Чтобы складывать или вычитать дроби с разными знаменателями, нужно привести их к общему знаменателю. При умножении и делении смешанные числа сначала переводим в неправильные дроби.
а) $\frac{1}{5} + \frac{1}{3} = \frac{3}{15} + \frac{5}{15} = \frac{8}{15}$
б) $\frac{1}{2} + \frac{3}{8} = \frac{4}{8} + \frac{3}{8} = \frac{7}{8}$
в) $\frac{3}{4} + 2 = 2 \frac{3}{4} = \frac{11}{4}$
г) $\frac{2}{3} - \frac{1}{6} = \frac{4}{6} - \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$
д) $\frac{7}{12} - 1 = \frac{7}{12} - \frac{12}{12} = -\frac{5}{12}$
е) $\frac{4}{5} - \frac{9}{10} = \frac{8}{10} - \frac{9}{10} = -\frac{1}{10}$
ё) $\frac{1}{3} - \frac{1}{2} = \frac{2}{6} - \frac{3}{6} = -\frac{1}{6}$
ж) $1 + \frac{7}{3} = \frac{3}{3} + \frac{7}{3} = \frac{10}{3} = 3 \frac{1}{3}$
з) $\frac{8}{15} : 4 = \frac{8}{15} \cdot \frac{1}{4} = \frac{2}{15}$
и) $3 : \frac{3}{2} = 3 \cdot \frac{2}{3} = 2$
й) $-1 : \frac{3}{4} = -1 \cdot \frac{4}{3} = -\frac{4}{3} = -1 \frac{1}{3}$
к) $-\frac{7}{12} : (-\frac{1}{4}) = \frac{7}{12} \cdot 4 = \frac{7}{3} = 2 \frac{1}{3}$
л) $\frac{1}{4} \cdot 2 = \frac{2}{4} = \frac{1}{2}$
м) $-\frac{3}{4} \cdot \frac{4}{9} = -\frac{1}{3}$
н) $\frac{7}{9} \cdot \frac{18}{35} = \frac{1}{1} \cdot \frac{2}{5} = \frac{2}{5}$
о) $-\frac{4}{19} \cdot (-\frac{57}{64}) = \frac{1}{1} \cdot \frac{3}{16} = \frac{3}{16}$
п) $2 \frac{3}{4} + 3 \frac{5}{7} = \frac{11}{4} + \frac{26}{7} = \frac{77}{28} + \frac{104}{28} = \frac{181}{28} = 6 \frac{13}{28}$
р) $-4 \frac{2}{3} + 7 \frac{1}{2} = -\frac{14}{3} + \frac{15}{2} = -\frac{28}{6} + \frac{45}{6} = \frac{17}{6} = 2 \frac{5}{6}$
с) $4 \frac{1}{3} + \frac{3}{17} = \frac{13}{3} + \frac{3}{17} = \frac{221}{51} + \frac{9}{51} = \frac{230}{51} = 4 \frac{26}{51}$
т) $-5 \frac{2}{5} + 4 \frac{1}{3} = -\frac{27}{5} + \frac{13}{3} = -\frac{81}{15} + \frac{65}{15} = -\frac{16}{15} = -1 \frac{1}{15}$
у) $6 \frac{1}{2} - 3 \frac{3}{4} = \frac{13}{2} - \frac{15}{4} = \frac{26}{4} - \frac{15}{4} = \frac{11}{4} = 2 \frac{3}{4}$
ф) $2 \frac{1}{2} - 7 \frac{5}{6} = \frac{5}{2} - \frac{47}{6} = \frac{15}{6} - \frac{47}{6} = -\frac{32}{6} = -5 \frac{1}{3}$
х) $-4 \frac{2}{3} - 7 \frac{7}{9} = -\frac{14}{3} - \frac{70}{9} = -\frac{42}{9} - \frac{70}{9} = -\frac{112}{9} = -12 \frac{4}{9}$
ц) $-2 \frac{2}{3} - 3 \frac{5}{9} = -\frac{8}{3} - \frac{32}{9} = -\frac{24}{9} - \frac{32}{9} = -\frac{56}{9} = -6 \frac{2}{9}$
ч) $2 \frac{3}{4} \cdot 5 \frac{7}{33} = \frac{11}{4} \cdot \frac{172}{33} = \frac{1}{1} \cdot \frac{43}{3} = \frac{43}{3} = 14 \frac{1}{3}$
ш) $-3 \frac{1}{2} \cdot 2 \frac{2}{5} = -\frac{7}{2} \cdot \frac{12}{5} = -\frac{42}{5} = -8 \frac{2}{5}$
щ) $-4 \frac{5}{7} \cdot (-2 \frac{6}{11}) = -\frac{33}{7} \cdot (-\frac{28}{11}) = 3 \cdot 4 = 12$
ъ) $-3 \frac{1}{2} : 2 \frac{2}{7} = -\frac{7}{2} : \frac{16}{7} = -\frac{7}{2} \cdot \frac{7}{16} = -\frac{49}{32} = -1 \frac{17}{32}$
ы) $4 \frac{1}{3} : 2 \frac{5}{6} = \frac{13}{3} : \frac{17}{6} = \frac{13}{3} \cdot \frac{6}{17} = \frac{13}{1} \cdot \frac{2}{17} = \frac{26}{17} = 1 \frac{9}{17}$
ь) $-7 \frac{3}{8} : (-2 \frac{1}{16}) = -\frac{59}{8} : (-\frac{33}{16}) = \frac{59}{8} \cdot \frac{16}{33} = \frac{59}{1} \cdot \frac{2}{33} = \frac{118}{33} = 3 \frac{19}{33}$
э) $-1 \frac{1}{3} : 3 \frac{1}{6} = -\frac{4}{3} : \frac{19}{6} = -\frac{4}{3} \cdot \frac{6}{19} = -\frac{4}{1} \cdot \frac{2}{19} = -\frac{8}{19}$
ю) $4 \frac{1}{5} : 7 \frac{1}{25} = \frac{21}{5} : \frac{176}{25} = \frac{21}{5} \cdot \frac{25}{176} = \frac{21}{1} \cdot \frac{5}{176} = \frac{105}{176}$
