3. Найдите разность: 1) a) 5/6 - 1/2 б) 3/5 - 1/7 2) a) 4/9 - 1/3 б) 9/14 - 2/7 3) a) 5/8 - 1/4 б) 9/14 - 9/21 в) 8/15 - 1/2 г) 4/7 - 3/10 в) 19/100 - 1/10 г) 4/5 - 12/25 в) 7/20 - 7/30 г) 5/12 - 1/6

1) a)

$$ \frac{5}{6} - \frac{1}{2} = \frac{5}{6} - \frac{1 \cdot 3}{2 \cdot 3} = \frac{5}{6} - \frac{3}{6} = \frac{5-3}{6} = \frac{2}{6} = \frac{1}{3} $$

б)

$$ \frac{3}{5} - \frac{1}{7} = \frac{3 \cdot 7}{5 \cdot 7} - \frac{1 \cdot 5}{7 \cdot 5} = \frac{21}{35} - \frac{5}{35} = \frac{21-5}{35} = \frac{16}{35} $$

в)

$$ \frac{8}{15} - \frac{1}{2} = \frac{8 \cdot 2}{15 \cdot 2} - \frac{1 \cdot 15}{2 \cdot 15} = \frac{16}{30} - \frac{15}{30} = \frac{16-15}{30} = \frac{1}{30} $$

г)

$$ \frac{4}{7} - \frac{3}{10} = \frac{4 \cdot 10}{7 \cdot 10} - \frac{3 \cdot 7}{10 \cdot 7} = \frac{40}{70} - \frac{21}{70} = \frac{40-21}{70} = \frac{19}{70} $$

Ответ: 1) a) 1/3; б) 16/35; в) 1/30; г) 19/70

2) a)

$$ \frac{4}{9} - \frac{1}{3} = \frac{4}{9} - \frac{1 \cdot 3}{3 \cdot 3} = \frac{4}{9} - \frac{3}{9} = \frac{4-3}{9} = \frac{1}{9} $$

б)

$$ \frac{9}{14} - \frac{2}{7} = \frac{9}{14} - \frac{2 \cdot 2}{7 \cdot 2} = \frac{9}{14} - \frac{4}{14} = \frac{9-4}{14} = \frac{5}{14} $$

в)

$$ \frac{19}{100} - \frac{1}{10} = \frac{19}{100} - \frac{1 \cdot 10}{10 \cdot 10} = \frac{19}{100} - \frac{10}{100} = \frac{19-10}{100} = \frac{9}{100} $$

г)

$$ \frac{4}{5} - \frac{12}{25} = \frac{4 \cdot 5}{5 \cdot 5} - \frac{12}{25} = \frac{20}{25} - \frac{12}{25} = \frac{20-12}{25} = \frac{8}{25} $$

Ответ: 2) a) 1/9; б) 5/14; в) 9/100; г) 8/25

3) a)

$$ \frac{5}{8} - \frac{1}{4} = \frac{5}{8} - \frac{1 \cdot 2}{4 \cdot 2} = \frac{5}{8} - \frac{2}{8} = \frac{5-2}{8} = \frac{3}{8} $$

б)

$$ \frac{9}{14} - \frac{9}{21} = \frac{9 \cdot 3}{14 \cdot 3} - \frac{9 \cdot 2}{21 \cdot 2} = \frac{27}{42} - \frac{18}{42} = \frac{27-18}{42} = \frac{9}{42} = \frac{3}{14} $$

в)

$$ \frac{7}{20} - \frac{7}{30} = \frac{7 \cdot 3}{20 \cdot 3} - \frac{7 \cdot 2}{30 \cdot 2} = \frac{21}{60} - \frac{14}{60} = \frac{21-14}{60} = \frac{7}{60} $$

г)

$$ \frac{5}{12} - \frac{1}{6} = \frac{5}{12} - \frac{1 \cdot 2}{6 \cdot 2} = \frac{5}{12} - \frac{2}{12} = \frac{5-2}{12} = \frac{3}{12} = \frac{1}{4} $$

Ответ: 3) a) 3/8; б) 3/14; в) 7/60; г) 1/4