Question

Помогите пожалуйста!!! Дам 20 баллов

Answer 1

Ответ:

$1)\ \{ 1,\,\,2,\,\,3,\,\,4,\,\,5,\,\,6,\,\,7,\,\,8\};\\2)\ 4;\\ 3)\ \{ 8,\,\,9,\,\,10,\,\,11,\,\,12,\,\,13,\,\,14,\,\,15,\,\,16,\,\,17\};\\ 4)\ \{ 3,\,\,4\};\\ 5)\ \{ 14,\,\,15,\,\,16,\,\,17,\,\,18,\,\,19,\,\,20,\,\,21,\,\,22,\,\,23,\,\,24\};\\ 6)\ \{ 5,\,\,6,\, \ldots ,\,\,33\}$

Пошаговое объяснение:

В каждом из примеров приведем все три дроби к общему знаменателю, тогда можно сравнить между собой числители.

1)

$0 = \displaystyle\frac{0}{9};\,\,1 = \displaystyle\frac{9}{9}\,\, \Rightarrow \,\,\displaystyle\frac{0}{9} < \displaystyle\frac{a}{9} < \displaystyle\frac{9}{9};\\\\0 < a < 9;\\\\a \in \{ 1,\,\,2,\,\,3,\,\,4,\,\,5,\,\,6,\,\,7,\,\,8\} .$

2)

$\displaystyle\frac{1}{5} = \displaystyle\frac{3}{{15}};\,\,\displaystyle\frac{1}{3} = \displaystyle\frac{5}{{15}}\,\, \Rightarrow \,\,\displaystyle\frac{3}{{15}} < \displaystyle\frac{a}{{15}} < \displaystyle\frac{5}{{15}};\\\\3 < a < 5;\\\\a = 4.$

3)

$1 = \displaystyle\frac{{17}}{{17}}\,\, \Rightarrow \,\,\displaystyle\frac{8}{{17}} \le \displaystyle\frac{a}{{17}} \le \displaystyle\frac{{17}}{{17}};\\\\8 \le a \le 17;\\\\a \in \{ 8,\,\,9,\,\,10,\,\,11,\,\,12,\,\,13,\,\,14,\,\,15,\,\,16,\,\,17\} .$

4)

$1 = \displaystyle\frac{{24}}{{24}};\,\,\displaystyle\frac{a}{3} = \displaystyle\frac{{8a}}{{24}};\,\,1\displaystyle\frac{3}{8} = \displaystyle\frac{{11}}{8} = \displaystyle\frac{{33}}{{24}}\,\, \Rightarrow \,\,\displaystyle\frac{{24}}{{24}} \le \displaystyle\frac{{8a}}{{24}} < \displaystyle\frac{{33}}{{24}};\\\\24 \le 8a < 33;\\\\\displaystyle\frac{{24}}{8} \le a < \displaystyle\frac{{33}}{8}\\\\3 \le a < 4\displaystyle\frac{1}{8};\\\\a \in \{ 3,\,\,4\} .$

5)

$1 = \displaystyle\frac{{24}}{{24}}\,\, \Rightarrow \,\,\displaystyle\frac{{13}}{{24}} < \displaystyle\frac{a}{{24}} \le \displaystyle\frac{{24}}{{24}};\\\\13 < a \le 24;\\\\a \in \{ 14,\,\,15,\,\,16,\,\,17,\,\,18,\,\,19,\,\,20,\,\,21,\,\,22,\,\,23,\,\,24\} .$

6)

$\displaystyle\frac{1}{4} = \displaystyle\frac{9}{{36}};\,\,\displaystyle\frac{a}{{18}} = \displaystyle\frac{{2a}}{{36}};\,\,1\displaystyle\frac{5}{6} = \displaystyle\frac{{11}}{6} = \displaystyle\frac{{66}}{{36}}\,\, \Rightarrow \,\,\displaystyle\frac{9}{{36}} < \displaystyle\frac{{2a}}{{36}} \le \displaystyle\frac{{66}}{{36}};\\\\9 < 2a \le 66;\\\\\displaystyle\frac{9}{2} < a \le \displaystyle\frac{{66}}{2};\\\\4\displaystyle\frac{1}{2} < a \le 33;\\\\a \in \{ 5,\,\,6,\, \ldots ,\,\,33\} .$