4.234 Выполните вычитание: a) -2 5/8 – 1/4; б) 3/8 – 1 1/4; в) 1 3/5 – (-2 1/6); г) -3 7/12 – (-1 3/8); д) -3 1/4 – 0,75; e) -2,4 – (-1 1/3); ж) 3 2/11 – 4 7/33; з) -4 4/9 – (-3 5/6).

a) \(-2\frac{5}{8} - \frac{1}{4} = -\frac{2 \cdot 8 + 5}{8} - \frac{1}{4} = -\frac{21}{8} - \frac{1 \cdot 2}{4 \cdot 2} = -\frac{21}{8} - \frac{2}{8} = \frac{-21 - 2}{8} = \frac{-23}{8} = -2\frac{7}{8}\)

б) \(\frac{3}{8} - 1\frac{1}{4} = \frac{3}{8} - \frac{1 \cdot 4 + 1}{4} = \frac{3}{8} - \frac{5}{4} = \frac{3}{8} - \frac{5 \cdot 2}{4 \cdot 2} = \frac{3}{8} - \frac{10}{8} = \frac{3 - 10}{8} = \frac{-7}{8} = -\frac{7}{8}\)

в) \(1\frac{3}{5} - (-2\frac{1}{6}) = \frac{1 \cdot 5 + 3}{5} + \frac{2 \cdot 6 + 1}{6} = \frac{8}{5} + \frac{13}{6} = \frac{8 \cdot 6}{5 \cdot 6} + \frac{13 \cdot 5}{6 \cdot 5} = \frac{48}{30} + \frac{65}{30} = \frac{48 + 65}{30} = \frac{113}{30} = 3\frac{23}{30}\)

г) \(-3\frac{7}{12} - (-1\frac{3}{8}) = -\frac{3 \cdot 12 + 7}{12} + \frac{1 \cdot 8 + 3}{8} = -\frac{43}{12} + \frac{11}{8} = -\frac{43 \cdot 2}{12 \cdot 2} + \frac{11 \cdot 3}{8 \cdot 3} = -\frac{86}{24} + \frac{33}{24} = \frac{-86 + 33}{24} = \frac{-53}{24} = -2\frac{5}{24}\)

д) \(-3\frac{1}{4} - 0.75 = -3\frac{1}{4} - \frac{75}{100} = -3\frac{1}{4} - \frac{3}{4} = -\frac{3 \cdot 4 + 1}{4} - \frac{3}{4} = -\frac{13}{4} - \frac{3}{4} = \frac{-13 - 3}{4} = \frac{-16}{4} = -4\)

e) \(-2.4 - (-1\frac{1}{3}) = -2\frac{4}{10} + 1\frac{1}{3} = -2\frac{2}{5} + 1\frac{1}{3} = -\frac{2 \cdot 5 + 2}{5} + \frac{1 \cdot 3 + 1}{3} = -\frac{12}{5} + \frac{4}{3} = -\frac{12 \cdot 3}{5 \cdot 3} + \frac{4 \cdot 5}{3 \cdot 5} = -\frac{36}{15} + \frac{20}{15} = \frac{-36 + 20}{15} = \frac{-16}{15} = -1\frac{1}{15}\)

ж) \(3\frac{2}{11} - 4\frac{7}{33} = \frac{3 \cdot 11 + 2}{11} - \frac{4 \cdot 33 + 7}{33} = \frac{35}{11} - \frac{139}{33} = \frac{35 \cdot 3}{11 \cdot 3} - \frac{139}{33} = \frac{105}{33} - \frac{139}{33} = \frac{105 - 139}{33} = \frac{-34}{33} = -1\frac{1}{33}\)

з) \(-4\frac{4}{9} - (-3\frac{5}{6}) = -4\frac{4}{9} + 3\frac{5}{6} = -\frac{4 \cdot 9 + 4}{9} + \frac{3 \cdot 6 + 5}{6} = -\frac{40}{9} + \frac{23}{6} = -\frac{40 \cdot 2}{9 \cdot 2} + \frac{23 \cdot 3}{6 \cdot 3} = -\frac{80}{18} + \frac{69}{18} = \frac{-80 + 69}{18} = \frac{-11}{18} = -\frac{11}{18}\)