Карточка №5 Найдите значение выражения: 1. 1/2 - 13/50 2. 1/2 + 16/5 3. 27/3.2 4. 0,7/1+1/3 5. 1/1/36-1/44 6. (17/10 + 10/11) : 5/44 7. (9/16 +2 3/8) . 4 8. 1 1/12 : (1 13/18 -2 5/9) 9. 6.(1/3)^2 -14. 1/3 10. (14/11 + 5/22) . 9/10

Ответ:

1. \[\frac{1}{2} - \frac{13}{50} = \frac{25}{50} - \frac{13}{50} = \frac{25-13}{50} = \frac{12}{50} = \frac{6}{25} = 0.24\]

2. \[\frac{1}{2} + \frac{16}{5} = \frac{5}{10} + \frac{32}{10} = \frac{5+32}{10} = \frac{37}{10} = 3.7\]

3. \[\frac{27}{3.2} = \frac{270}{32} = \frac{135}{16} = 8 \frac{7}{16} = 8.4375\]

4. \[\frac{0.7}{1 + \frac{1}{3}} = \frac{0.7}{\frac{3}{3} + \frac{1}{3}} = \frac{0.7}{\frac{4}{3}} = 0.7 \cdot \frac{3}{4} = \frac{0.7 \cdot 3}{4} = \frac{2.1}{4} = 0.525\]

5. \[\frac{1}{\frac{1}{36} - \frac{1}{44}} = \frac{1}{\frac{11}{396} - \frac{9}{396}} = \frac{1}{\frac{2}{396}} = \frac{396}{2} = 198\]

6. \[\left(\frac{17}{10} + \frac{10}{11}\right) : \frac{5}{44} = \left(\frac{187}{110} + \frac{100}{110}\right) : \frac{5}{44} = \frac{287}{110} : \frac{5}{44} = \frac{287}{110} \cdot \frac{44}{5} = \frac{287 \cdot 4}{10 \cdot 5} = \frac{287 \cdot 2}{5 \cdot 5} = \frac{574}{25} = 22 \frac{24}{25} = 22.96\]

7. \[\left(\frac{9}{16} + 2 \frac{3}{8}\right) \cdot 4 = \left(\frac{9}{16} + \frac{19}{8}\right) \cdot 4 = \left(\frac{9}{16} + \frac{38}{16}\right) \cdot 4 = \frac{47}{16} \cdot 4 = \frac{47 \cdot 4}{16} = \frac{47}{4} = 11 \frac{3}{4} = 11.75\]

8. \[1 \frac{1}{12} : \left(1 \frac{13}{18} - 2 \frac{5}{9}\right) = \frac{13}{12} : \left(\frac{31}{18} - \frac{23}{9}\right) = \frac{13}{12} : \left(\frac{31}{18} - \frac{46}{18}\right) = \frac{13}{12} : \frac{-15}{18} = \frac{13}{12} \cdot \frac{18}{-15} = \frac{13}{2} \cdot \frac{3}{-15} = \frac{13}{2} \cdot \frac{1}{-5} = \frac{13}{-10} = -1.3\]

9. \[6 \cdot \left(\frac{1}{3}\right)^2 - 14 \cdot \frac{1}{3} = 6 \cdot \frac{1}{9} - \frac{14}{3} = \frac{6}{9} - \frac{14}{3} = \frac{2}{3} - \frac{14}{3} = \frac{2-14}{3} = \frac{-12}{3} = -4\]

10. \[\left(\frac{14}{11} + \frac{5}{22}\right) \cdot \frac{9}{10} = \left(\frac{28}{22} + \frac{5}{22}\right) \cdot \frac{9}{10} = \frac{33}{22} \cdot \frac{9}{10} = \frac{3}{2} \cdot \frac{9}{10} = \frac{27}{20} = 1.35\]

Ответ: