в) 3/5 - 4/15 = г) 7/8 - 6/7 = ж) 7/15 - 8/25 = з) 7/45 - 7/60 = а) 1/6 + 5/9 + 5/6 + 4/9 = б) 2/17 + 3/8 + 5/17 + 10/17 + 5/8 = в) 1/12 + 1/16 + 5/12 + 7/16 = г) 3/17 + 4/5 + 1/15 + 14/17 = а) x + 3/16 = 17/20 x = 17/20 ... 3/16 б) 8/15 + y = 7/12 y + 7/12 ... 8/15

Решение примеров на вычитание дробей

в) \(\frac{3}{5} - \frac{4}{15} = \frac{3 \cdot 3}{5 \cdot 3} - \frac{4}{15} = \frac{9}{15} - \frac{4}{15} = \frac{9 - 4}{15} = \frac{5}{15} = \frac{1}{3}\)

г) \(\frac{7}{8} - \frac{6}{7} = \frac{7 \cdot 7}{8 \cdot 7} - \frac{6 \cdot 8}{7 \cdot 8} = \frac{49}{56} - \frac{48}{56} = \frac{49 - 48}{56} = \frac{1}{56}\)

ж) \(\frac{7}{15} - \frac{8}{25} = \frac{7 \cdot 5}{15 \cdot 5} - \frac{8 \cdot 3}{25 \cdot 3} = \frac{35}{75} - \frac{24}{75} = \frac{35 - 24}{75} = \frac{11}{75}\)

з) \(\frac{7}{45} - \frac{7}{60} = \frac{7 \cdot 4}{45 \cdot 4} - \frac{7 \cdot 3}{60 \cdot 3} = \frac{28}{180} - \frac{21}{180} = \frac{28 - 21}{180} = \frac{7}{180}\)

Решение примеров на сложение дробей

a) \(\frac{1}{6} + \frac{5}{9} + \frac{5}{6} + \frac{4}{9} = (\frac{1}{6} + \frac{5}{6}) + (\frac{5}{9} + \frac{4}{9}) = \frac{6}{6} + \frac{9}{9} = 1 + 1 = 2\)

б) \(\frac{2}{17} + \frac{3}{8} + \frac{5}{17} + \frac{10}{17} + \frac{5}{8} = (\frac{2}{17} + \frac{5}{17} + \frac{10}{17}) + (\frac{3}{8} + \frac{5}{8}) = \frac{17}{17} + \frac{8}{8} = 1 + 1 = 2\)

в) \(\frac{1}{12} + \frac{1}{16} + \frac{5}{12} + \frac{7}{16} = (\frac{1}{12} + \frac{5}{12}) + (\frac{1}{16} + \frac{7}{16}) = \frac{6}{12} + \frac{8}{16} = \frac{1}{2} + \frac{1}{2} = 1\)

г) \(\frac{3}{17} + \frac{4}{5} + \frac{1}{15} + \frac{14}{17} = (\frac{3}{17} + \frac{14}{17}) + (\frac{4}{5} + \frac{1}{15}) = \frac{17}{17} + \frac{4 \cdot 3}{5 \cdot 3} + \frac{1}{15} = 1 + \frac{12}{15} + \frac{1}{15} = 1 + \frac{13}{15} = 1 \frac{13}{15}\)

Решение уравнений

a) \(x + \frac{3}{16} = \frac{17}{20}\)

\(x = \frac{17}{20} - \frac{3}{16}\)

\(x = \frac{17 \cdot 4}{20 \cdot 4} - \frac{3 \cdot 5}{16 \cdot 5}\)

\(x = \frac{68}{80} - \frac{15}{80}\)

\(x = \frac{53}{80}\)

б) \(\frac{8}{15} + y = \frac{7}{12}\)

\(y = \frac{7}{12} - \frac{8}{15}\)

\(y = \frac{7 \cdot 5}{12 \cdot 5} - \frac{8 \cdot 4}{15 \cdot 4}\)

\(y = \frac{35}{60} - \frac{32}{60}\)

\(y = \frac{3}{60} = \frac{1}{20}\)