№ 4. Выполните вычитание: a) 6/7 - 9/14 д) 5/9 - 3/8 и) 7/18 - 1/45 б) 9/20 - 5/12 е) 7/9 - 5/12 к) 11/42 - 5/28 в) 6/7 - 2/3 ж) 7/12 - 3/8 л) 9/14 - 19/35 г) 11/12 - 5/6 з) 1/10 - 1/12 м) 9/20 - 1/30

a) \(\frac{6}{7} - \frac{9}{14}\). НОЗ (7, 14) = 14

$$\frac{6}{7} - \frac{9}{14} = \frac{6 \cdot 2}{7 \cdot 2} - \frac{9}{14} = \frac{12}{14} - \frac{9}{14} = \frac{12-9}{14} = \frac{3}{14}$$

Ответ: $$\frac{3}{14}$$

д) \(\frac{5}{9} - \frac{3}{8}\). НОЗ (9, 8) = 72

$$\frac{5}{9} - \frac{3}{8} = \frac{5 \cdot 8}{9 \cdot 8} - \frac{3 \cdot 9}{8 \cdot 9} = \frac{40}{72} - \frac{27}{72} = \frac{40-27}{72} = \frac{13}{72}$$

Ответ: $$\frac{13}{72}$$

и) \(\frac{7}{18} - \frac{1}{45}\). НОЗ (18, 45) = 90

$$\frac{7}{18} - \frac{1}{45} = \frac{7 \cdot 5}{18 \cdot 5} - \frac{1 \cdot 2}{45 \cdot 2} = \frac{35}{90} - \frac{2}{90} = \frac{35-2}{90} = \frac{33}{90} = \frac{11}{30}$$

Ответ: $$\frac{11}{30}$$

б) \(\frac{9}{20} - \frac{5}{12}\). НОЗ (20, 12) = 60

$$\frac{9}{20} - \frac{5}{12} = \frac{9 \cdot 3}{20 \cdot 3} - \frac{5 \cdot 5}{12 \cdot 5} = \frac{27}{60} - \frac{25}{60} = \frac{27-25}{60} = \frac{2}{60} = \frac{1}{30}$$

Ответ: $$\frac{1}{30}$$

е) \(\frac{7}{9} - \frac{5}{12}\). НОЗ (9, 12) = 36

$$\frac{7}{9} - \frac{5}{12} = \frac{7 \cdot 4}{9 \cdot 4} - \frac{5 \cdot 3}{12 \cdot 3} = \frac{28}{36} - \frac{15}{36} = \frac{28-15}{36} = \frac{13}{36}$$

Ответ: $$\frac{13}{36}$$

к) \(\frac{11}{42} - \frac{5}{28}\). НОЗ (42, 28) = 84

$$\frac{11}{42} - \frac{5}{28} = \frac{11 \cdot 2}{42 \cdot 2} - \frac{5 \cdot 3}{28 \cdot 3} = \frac{22}{84} - \frac{15}{84} = \frac{22-15}{84} = \frac{7}{84} = \frac{1}{12}$$

Ответ: $$\frac{1}{12}$$

в) \(\frac{6}{7} - \frac{2}{3}\). НОЗ (7, 3) = 21

$$\frac{6}{7} - \frac{2}{3} = \frac{6 \cdot 3}{7 \cdot 3} - \frac{2 \cdot 7}{3 \cdot 7} = \frac{18}{21} - \frac{14}{21} = \frac{18-14}{21} = \frac{4}{21}$$

Ответ: $$\frac{4}{21}$$

ж) \(\frac{7}{12} - \frac{3}{8}\). НОЗ (12, 8) = 24

$$\frac{7}{12} - \frac{3}{8} = \frac{7 \cdot 2}{12 \cdot 2} - \frac{3 \cdot 3}{8 \cdot 3} = \frac{14}{24} - \frac{9}{24} = \frac{14-9}{24} = \frac{5}{24}$$

Ответ: $$\frac{5}{24}$$

л) \(\frac{9}{14} - \frac{19}{35}\). НОЗ (14, 35) = 70

$$\frac{9}{14} - \frac{19}{35} = \frac{9 \cdot 5}{14 \cdot 5} - \frac{19 \cdot 2}{35 \cdot 2} = \frac{45}{70} - \frac{38}{70} = \frac{45-38}{70} = \frac{7}{70} = \frac{1}{10}$$

Ответ: $$\frac{1}{10}$$

г) \(\frac{11}{12} - \frac{5}{6}\). НОЗ (12, 6) = 12

$$\frac{11}{12} - \frac{5}{6} = \frac{11}{12} - \frac{5 \cdot 2}{6 \cdot 2} = \frac{11}{12} - \frac{10}{12} = \frac{11-10}{12} = \frac{1}{12}$$

Ответ: $$\frac{1}{12}$$

з) \(\frac{1}{10} - \frac{1}{12}\). НОЗ (10, 12) = 60

$$\frac{1}{10} - \frac{1}{12} = \frac{1 \cdot 6}{10 \cdot 6} - \frac{1 \cdot 5}{12 \cdot 5} = \frac{6}{60} - \frac{5}{60} = \frac{6-5}{60} = \frac{1}{60}$$

Ответ: $$\frac{1}{60}$$

м) \(\frac{9}{20} - \frac{1}{30}\). НОЗ (20, 30) = 60

$$\frac{9}{20} - \frac{1}{30} = \frac{9 \cdot 3}{20 \cdot 3} - \frac{1 \cdot 2}{30 \cdot 2} = \frac{27}{60} - \frac{2}{60} = \frac{27-2}{60} = \frac{25}{60} = \frac{5}{12}$$

Ответ: $$\frac{5}{12}$$