Карточка №4 Найдите значение выражения: 1. 1/5 - 27/20 2. 2/25 + 1/4 3. 14/5.4 4. 1,8/1+1/11 5. 1/1/63+1/72 6. (17/35 + 3/8) : 5/28 7. (5/6 + 3/5) .24 8. 3 7/11 : (2/11 +2 4/19) 9. 7.(1/7)^2 -8. 1/7 10. (1/20 + 11/8) . 18/5

Ответ:

1. \[\frac{1}{5} - \frac{27}{20} = \frac{4}{20} - \frac{27}{20} = \frac{4-27}{20} = \frac{-23}{20} = -1 \frac{3}{20}\]

2. \[\frac{2}{25} + \frac{1}{4} = \frac{8}{100} + \frac{25}{100} = \frac{8+25}{100} = \frac{33}{100}\]

3. \[\frac{14}{5 \cdot 4} = \frac{14}{20} = \frac{7}{10} = 0.7\]

4. \[\frac{1.8}{1 + \frac{1}{11}} = \frac{1.8}{\frac{11}{11} + \frac{1}{11}} = \frac{1.8}{\frac{12}{11}} = \frac{1.8}{1} \cdot \frac{11}{12} = \frac{1.8 \cdot 11}{12} = \frac{19.8}{12} = 1.65\]

5. \[\frac{1}{\frac{1}{63} + \frac{1}{72}} = \frac{1}{\frac{8}{504} + \frac{7}{504}} = \frac{1}{\frac{15}{504}} = \frac{504}{15} = \frac{168}{5} = 33 \frac{3}{5} = 33.6\]

6. \[\left(\frac{17}{35} + \frac{3}{8}\right) : \frac{5}{28} = \left(\frac{136}{280} + \frac{105}{280}\right) : \frac{5}{28} = \frac{241}{280} : \frac{5}{28} = \frac{241}{280} \cdot \frac{28}{5} = \frac{241}{10 \cdot 5} = \frac{241}{50} = 4 \frac{41}{50} = 4.82\]

7. \[\left(\frac{5}{6} + \frac{3}{5}\right) \cdot 24 = \left(\frac{25}{30} + \frac{18}{30}\right) \cdot 24 = \frac{43}{30} \cdot 24 = \frac{43 \cdot 24}{30} = \frac{43 \cdot 4}{5} = \frac{172}{5} = 34 \frac{2}{5} = 34.4\]

8. \[3 \frac{7}{11} : \left(\frac{2}{11} + 2 \frac{4}{19}\right) = \frac{40}{11} : \left(\frac{2}{11} + \frac{42}{19}\right) = \frac{40}{11} : \left(\frac{38}{209} + \frac{462}{209}\right) = \frac{40}{11} : \frac{500}{209} = \frac{40}{11} \cdot \frac{209}{500} = \frac{40 \cdot 19}{500} = \frac{4 \cdot 19}{50} = \frac{76}{50} = \frac{38}{25} = 1 \frac{13}{25} = 1.52\]

9. \[7 \cdot \left(\frac{1}{7}\right)^2 - 8 \cdot \frac{1}{7} = 7 \cdot \frac{1}{49} - \frac{8}{7} = \frac{7}{49} - \frac{8}{7} = \frac{1}{7} - \frac{8}{7} = \frac{1-8}{7} = \frac{-7}{7} = -1\]

10. \[\left(\frac{1}{20} + \frac{11}{8}\right) \cdot \frac{18}{5} = \left(\frac{2}{40} + \frac{55}{40}\right) \cdot \frac{18}{5} = \frac{57}{40} \cdot \frac{18}{5} = \frac{57 \cdot 9}{20 \cdot 5} = \frac{513}{100} = 5 \frac{13}{100} = 5.13\]

Ответ: