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)

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

2)

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

3)

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

4)

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

Ответ:

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