1. Выполните действия: а) 1/12 + 5/6 б) 2 - 1 7/8 в) 2 1/4 : 1 1/2 г) 12 - 3/4

Решение:

1. а)
   

   \[ \frac{1}{12} + \frac{5}{6} = \frac{1}{12} + \frac{5 \times 2}{6 \times 2} = \frac{1}{12} + \frac{10}{12} = \frac{1+10}{12} = \frac{11}{12} \]

   
   


2. б)
   

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

   
   


3. в)
   

   \[ 2\frac{1}{4} : 1\frac{1}{2} = \frac{2 \times 4 + 1}{4} : \frac{1 \times 2 + 1}{2} = \frac{9}{4} : \frac{3}{2} = \frac{9}{4} \times \frac{2}{3} = \frac{9 \times 2}{4 \times 3} = \frac{18}{12} = \frac{3}{2} = 1\frac{1}{2} \]

   
   


4. г)
   

   \[ 12 - \frac{3}{4} = \frac{12 \times 4}{4} - \frac{3}{4} = \frac{48}{4} - \frac{3}{4} = \frac{48-3}{4} = \frac{45}{4} = 11\frac{1}{4} \]

   
   

Ответ: а) 11/12, б) 1/8, в) 1 1/2, г) 11 1/4