Вариант 1 1. Вычислите: a) 1/5 + 3/7 б) 4 3/14 - 1 2/21 в) 3 5/6 + 2 7/15 - 1 29/30 2. Вычислите: a) 4 2/3 * 3/5 б) 10 1/3 : 1 4/11 в) 2 2/5 * 1 1/6 : 6 2/3 3. Вычислите: a) 3/11 + 2/3 б) 2/3 : 5/7 в) 7/16 + 1/2 г) 5/12 - 15/15 4. Посадили 56 семян, 7/8 посаженных семян

Решение:

1. Вычисление:

1. a)
   

   \[ \frac{1}{5} + \frac{3}{7} = \frac{1 \times 7 + 3 \times 5}{5 \times 7} = \frac{7 + 15}{35} = \frac{22}{35} \]

2. б)
   

   \[ 4 \frac{3}{14} - 1 \frac{2}{21} = \frac{4 \times 14 + 3}{14} - \frac{1 \times 21 + 2}{21} = \frac{59}{14} - \frac{23}{21} \]

   Приводим к общему знаменателю 42:

   
   

   \[ \frac{59 \times 3}{14 \times 3} - \frac{23 \times 2}{21 \times 2} = \frac{177}{42} - \frac{46}{42} = \frac{177 - 46}{42} = \frac{131}{42} = 3 \frac{5}{42} \]

3. в)
   

   \[ 3 \frac{5}{6} + 2 \frac{7}{15} - 1 \frac{29}{30} = \frac{3 \times 6 + 5}{6} + \frac{2 \times 15 + 7}{15} - \frac{1 \times 30 + 29}{30} = \frac{23}{6} + \frac{37}{15} - \frac{59}{30} \]

   Приводим к общему знаменателю 30:

   
   

   \[ \frac{23 \times 5}{6 \times 5} + \frac{37 \times 2}{15 \times 2} - \frac{59}{30} = \frac{115}{30} + \frac{74}{30} - \frac{59}{30} = \frac{115 + 74 - 59}{30} = \frac{189 - 59}{30} = \frac{130}{30} = \frac{13}{3} = 4 \frac{1}{3} \]

2. Вычисление:

1. a)
   

   \[ 4 \frac{2}{3} \times \frac{3}{5} = \frac{4 \times 3 + 2}{3} \times \frac{3}{5} = \frac{14}{3} \times \frac{3}{5} = \frac{14 \times 3}{3 \times 5} = \frac{14}{5} = 2 \frac{4}{5} \]

2. б)
   

   \[ 10 \frac{1}{3} : 1 \frac{4}{11} = \frac{10 \times 3 + 1}{3} : \frac{1 \times 11 + 4}{11} = \frac{31}{3} : \frac{15}{11} = \frac{31}{3} \times \frac{11}{15} = \frac{31 \times 11}{3 \times 15} = \frac{341}{45} = 7 \frac{26}{45} \]

3. в)
   

   \[ 2 \frac{2}{5} \times 1 \frac{1}{6} : 6 \frac{2}{3} = \frac{2 \times 5 + 2}{5} \times \frac{1 \times 6 + 1}{6} : \frac{6 \times 3 + 2}{3} = \frac{12}{5} \times \frac{7}{6} : \frac{20}{3} \]

   \[ \left( \frac{12}{5} \times \frac{7}{6} \right) : \frac{20}{3} = \left( \frac{12 \times 7}{5 \times 6} \right) : \frac{20}{3} = \left( \frac{2 \times 7}{5} \right) : \frac{20}{3} = \frac{14}{5} : \frac{20}{3} \]

   \[ \frac{14}{5} \times \frac{3}{20} = \frac{14 \times 3}{5 \times 20} = \frac{42}{100} = \frac{21}{50} \]

3. Вычисление:

1. a)
   

   \[ \frac{3}{11} + \frac{2}{3} = \frac{3 \times 3 + 2 \times 11}{11 \times 3} = \frac{9 + 22}{33} = \frac{31}{33} \]

2. б)
   

   \[ \frac{2}{3} : \frac{5}{7} = \frac{2}{3} \times \frac{7}{5} = \frac{2 \times 7}{3 \times 5} = \frac{14}{15} \]

3. в)
   

   \[ \frac{7}{16} + \frac{1}{2} = \frac{7}{16} + \frac{1 \times 8}{2 \times 8} = \frac{7}{16} + \frac{8}{16} = \frac{7 + 8}{16} = \frac{15}{16} \]

4. г)
   

   \[ \frac{5}{12} - \frac{15}{15} = \frac{5}{12} - 1 = \frac{5}{12} - \frac{12}{12} = \frac{5 - 12}{12} = -\frac{7}{12} \]

4. Нахождение количества:

\[ 56 \times \frac{7}{8} = \frac{56 \times 7}{8} = 7 \times 7 = 49 \text{ семян} \]

Ответ: 49 семян.