Решение:

a)

$$12\frac{8}{9}:4+\frac{2}{3}\cdot \frac{1}{24}=\frac{116}{9}:4+\frac{2}{3}\cdot \frac{1}{24}=\frac{116}{9}\cdot \frac{1}{4}+\frac{2}{72}=\frac{29}{9}+\frac{1}{36}=\frac{29\cdot 4}{9\cdot 4}+ \frac{1}{36}=\frac{116}{36}+\frac{1}{36}=\frac{117}{36}=\frac{13}{4}=3\frac{1}{4}$$.

Ответ: $$3\frac{1}{4}$$

б)

$$(\frac{1}{4}+\frac{7}{18})\cdot 1\frac{1}{23}-1=(\frac{9}{36}+\frac{14}{36})\cdot \frac{24}{23}-1=\frac{23}{36}\cdot \frac{24}{23}-1=\frac{23\cdot 24}{36\cdot 23}-1=\frac{24}{36}-1=\frac{2}{3}-1=\frac{2}{3}-\frac{3}{3}=-\frac{1}{3}$$.

Ответ: $$-\frac{1}{3}$$

в)

$$5-(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5})=5-(\frac{30}{60}+\frac{20}{60}+\frac{15}{60}+\frac{12}{60})=5-\frac{30+20+15+12}{60}=5-\frac{77}{60}=\frac{300}{60}-\frac{77}{60}=\frac{223}{60}=3\frac{43}{60}$$.

Ответ: $$3\frac{43}{60}$$

г)

$$1\frac{5}{11}:1\frac{1}{11}-1\frac{1}{9}\cdot 1\frac{1}{5}-7\frac{5}{7}=\frac{16}{11}:\frac{12}{11}-\frac{10}{9}\cdot \frac{6}{5}-\frac{54}{7}=\frac{16}{11}\cdot \frac{11}{12}-\frac{10}{9}\cdot \frac{6}{5}-\frac{54}{7}=\frac{16}{12}-\frac{60}{45}-\frac{54}{7}=\frac{4}{3}-\frac{4}{3}-\frac{54}{7}=0-\frac{54}{7}=-\frac{54}{7}=-7\frac{5}{7}$$.

Ответ: $$-7\frac{5}{7}$$

д)

$$(3\frac{3}{7}\cdot 2\frac{5}{8}-16):5\frac{1}{4}+11\frac{11}{15}=(\frac{24}{7}\cdot \frac{21}{8}-16):\frac{21}{4}+\frac{176}{15}=(\frac{24\cdot 21}{7\cdot 8}-16):\frac{21}{4}+\frac{176}{15}=(\frac{3\cdot 3}{1}-16):\frac{21}{4}+\frac{176}{15}=(9-16):\frac{21}{4}+\frac{176}{15}=-7:\frac{21}{4}+\frac{176}{15}=-7\cdot \frac{4}{21}+\frac{176}{15}=-\frac{28}{21}+\frac{176}{15}=-\frac{4}{3}+\frac{176}{15}=-\frac{20}{15}+\frac{176}{15}=\frac{156}{15}=\frac{52}{5}=10\frac{2}{5}$$.

Ответ: $$10\frac{2}{5}$$

e)

$$4\frac{56}{157}+\frac{17}{139}:(\frac{9}{20}-\frac{1}{4}-\frac{1}{5})=4\frac{56}{157}+\frac{17}{139}:(\frac{9}{20}-\frac{5}{20}-\frac{4}{20})=4\frac{56}{157}+\frac{17}{139}:\frac{9-5-4}{20}=4\frac{56}{157}+\frac{17}{139}:0$$.

Деление на ноль не определено.

Ответ: не определено