7. Найдите значение выражения. a) 6:(1+2/3) б) 17:(1-3/4) в) 12-3:24/5 г) 110:7/22-5/22

Решаем по пунктам:

1. а)
   

   \[ 6 : \left( 1 + \frac{2}{3} \right) = 6 : \left( \frac{3}{3} + \frac{2}{3} \right) = 6 : \frac{5}{3} = 6 \times \frac{3}{5} = \frac{18}{5} = 3 \frac{3}{5} \]

2. б)
   

   \[ 17 : \left( 1 - \frac{3}{4} \right) = 17 : \left( \frac{4}{4} - \frac{3}{4} \right) = 17 : \frac{1}{4} = 17 \times 4 = 68 \]

3. в)
   

   \[ 12 - 3 : \frac{24}{5} = 12 - 3 \times \frac{5}{24} = 12 - \frac{15}{24} = 12 - \frac{5}{8} = \frac{96}{8} - \frac{5}{8} = \frac{91}{8} = 11 \frac{3}{8} \]

4. г)
   

   \[ \frac{10}{11} : \frac{7}{22} - \frac{5}{22} = \frac{10}{11} \times \frac{22}{7} - \frac{5}{22} = \frac{10 \times 2}{7} - \frac{5}{22} = \frac{20}{7} - \frac{5}{22} = \frac{20 \times 22}{7 \times 22} - \frac{5 \times 7}{22 \times 7} = \frac{440}{154} - \frac{35}{154} = \frac{405}{154} \]

Ответ:

• а) 3 3/5
• б) 68
• в) 11 3/8
• г) 405/154