Вариант № 3 1. Сократите дроби: а) 35; 6) 70; в) 84 42 84 56 2. Сравните дроби: а)-и; б) и 2222; в); 524 16 24 29" 27 33" 22; г) 24" 25 3. Выполните действия: 75. a)+; 6) +13 7; в) 195+2; 86 16 24 20 12 5 3 г) 5 40 (금) (금)

Вариант №3

1. Сократите дроби:

• а) \[\frac{35}{42} = \frac{5 \cdot 7}{6 \cdot 7} = \frac{5}{6}\]
• б) \[\frac{70}{84} = \frac{5 \cdot 14}{6 \cdot 14} = \frac{5}{6}\]
• в) \[\frac{84}{56} = \frac{12 \cdot 7}{8 \cdot 7} = \frac{12}{8} = \frac{3 \cdot 4}{2 \cdot 4} = \frac{3}{2}\]

2. Сравните дроби:

• а) \[\frac{3}{16} \ \text{и} \ \frac{5}{24} = \frac{3 \cdot 3}{16 \cdot 3} \ \text{и} \ \frac{5 \cdot 2}{24 \cdot 2} = \frac{9}{48} < \frac{10}{48} \Rightarrow \frac{3}{16} < \frac{5}{24}\]
• б) \[\frac{22}{29} \ \text{и} \ \frac{22}{27} = \frac{22 \cdot 27}{29 \cdot 27} \ \text{и} \ \frac{22 \cdot 29}{27 \cdot 29} = \frac{594}{783} < \frac{638}{783} \Rightarrow \frac{22}{29} < \frac{22}{27}\]
• в) \[\frac{13}{33} \ \text{и} \ \frac{9}{22} = \frac{13 \cdot 2}{33 \cdot 2} \ \text{и} \ \frac{9 \cdot 3}{22 \cdot 3} = \frac{26}{66} < \frac{27}{66} \Rightarrow \frac{13}{33} < \frac{9}{22}\]
• г) \[\frac{25}{24} \ \text{и} \ \frac{24}{25} = \frac{25 \cdot 25}{24 \cdot 25} \ \text{и} \ \frac{24 \cdot 24}{25 \cdot 24} = \frac{625}{600} > \frac{576}{600} \Rightarrow \frac{25}{24} > \frac{24}{25}\]

3. Выполните действия:

• а) \[\frac{7}{8} + \frac{5}{6} = \frac{7 \cdot 3}{8 \cdot 3} + \frac{5 \cdot 4}{6 \cdot 4} = \frac{21}{24} + \frac{20}{24} = \frac{41}{24} = 1\frac{17}{24}\]
• б) \[\frac{13}{16} + \frac{7}{24} = \frac{13 \cdot 3}{16 \cdot 3} + \frac{7 \cdot 2}{24 \cdot 2} = \frac{39}{48} + \frac{14}{48} = \frac{53}{48} = 1\frac{5}{48}\]
• в) \[\frac{19}{20} - \frac{5}{12} + \frac{2}{5} = \frac{19 \cdot 3}{20 \cdot 3} - \frac{5 \cdot 5}{12 \cdot 5} + \frac{2 \cdot 12}{5 \cdot 12} = \frac{57}{60} - \frac{25}{60} + \frac{24}{60} = \frac{56}{60} = \frac{14 \cdot 4}{15 \cdot 4} = \frac{14}{15}\]
• г) \[5\frac{3}{40} + (6\frac{7}{12} - 4\frac{8}{15}) = 5\frac{3}{40} + (6\frac{35}{60} - 4\frac{32}{60}) = 5\frac{3}{40} + 2\frac{3}{60} = 5\frac{9}{120} + 2\frac{6}{120} = 7\frac{15}{120} = 7\frac{1}{8}\]