Вычислите: 1) 11  \frac{17}{55} - 15,3; 2) 3 \frac{4}{7} \cdot 4,5 \cdot \frac{7}{35} \cdot 8,75 : \frac{2}{5} : \frac{9}{32}; 3) 19 \cdot 2 \frac{55}{76} - 39,4; 4) 6,8 \cdot \frac{5}{13} \cdot 2,7 \cdot 3 \frac{3}{25} : 5 \frac{2}{5} : \frac{1}{175}.

Решение:

1)

• \[ 11 \frac{17}{55} = \frac{11 \times 55 + 17}{55} = \frac{605 + 17}{55} = \frac{622}{55} \]
• \[ 15,3 = \frac{153}{10} \]
• \[ \frac{622}{55} - \frac{153}{10} = \frac{622 imes 2 - 153 imes 11}{110} = \frac{1244 - 1683}{110} = \frac{-439}{110} = -3 \frac{109}{110} \]

2)

• \[ 3 \frac{4}{7} = \frac{25}{7} \]
• \[ \frac{7}{35} = \frac{1}{5} \]
• \[ 4,5 = \frac{9}{2} \]
• \[ 8,75 = \frac{875}{100} = \frac{35}{4} \]
• \[ 5 \frac{2}{5} = \frac{27}{5} \]
• \[ \frac{25}{7} \times \frac{9}{2} \times \frac{1}{5} \times \frac{35}{4} : \frac{27}{5} : \frac{9}{32} \]
• \[ = \left( \frac{25}{7} \times \frac{9}{2} \times \frac{1}{5} \times \frac{35}{4} \right) \times \frac{5}{27} \times \frac{32}{9} \]
• \[ = \frac{25 imes 9 \times 1 imes 35 \times 5 imes 32}{7 \times 2 imes 5 imes 4 imes 27 imes 9} \]
• \[ = \frac{25 imes 1 imes 1 imes 5 imes 5 imes 32}{1 imes 2 imes 1 imes 4 imes 3 imes 1} \]
• \[ = \frac{25 imes 5 imes 5 imes 32}{2 imes 4 imes 3} = \frac{25 imes 25 imes 32}{24} = \frac{625 imes 4}{3} = \frac{2500}{3} = 833 \frac{1}{3} \]

3)

• \[ 2 \frac{55}{76} = \frac{2 imes 76 + 55}{76} = \frac{152 + 55}{76} = \frac{207}{76} \]
• \[ 19 \times \frac{207}{76} = \frac{19 imes 207}{76} = \frac{1 imes 207}{4} = \frac{207}{4} = 51,75 \]
• \[ 51,75 - 39,4 = 12,35 \]

4)

• \[ 6,8 = \frac{68}{10} = \frac{34}{5} \]
• \[ 2,7 = \frac{27}{10} \]
• \[ 3 \frac{3}{25} = \frac{78}{25} \]
• \[ 5 \frac{2}{5} = \frac{27}{5} \]
• \[ \frac{34}{5} \times \frac{5}{13} \times \frac{27}{10} \times \frac{78}{25} : \frac{27}{5} : \frac{1}{175} \]
• \[ = \left( \frac{34}{5} \times \frac{5}{13} \times \frac{27}{10} \times \frac{78}{25} \right) \times \frac{5}{27} \times 175 \]
• \[ = \frac{34 imes 5 imes 27 imes 78 imes 5 imes 175}{5 imes 13 imes 10 imes 25 imes 27} \]
• \[ = \frac{34 imes 1 imes 1 imes 78 imes 5 imes 175}{1 imes 13 imes 10 imes 25 imes 1} \]
• \[ = \frac{34 imes 78 imes 5 imes 175}{13 imes 10 imes 25} \]
• \[ = \frac{34 imes 6 imes 5 imes 175}{1 imes 10 imes 25} \]
• \[ = \frac{34 imes 6 imes 5 imes 7}{1 imes 2 imes 5} \]
• \[ = 34 imes 3 imes 7 = 102 imes 7 = 714 \]

Ответ:

• 1) -3 \frac{109}{110}
• 2) 833 \frac{1}{3}
• 3) 12,35
• 4) 714