2.276. Выполните действия: а) \((\frac49+\frac5{12})\cdot\frac{18}{31}\); б) \(\frac6{25}\cdot(\frac{11}{15}-\frac9{20})\); в) \((4-3\frac7{15})\cdot\frac58\); г) \((5-4\frac47)\cdot(7\frac16-6\frac5{12})\); д) \((1\frac1{24}-\frac5{12})\cdot(4\frac18-3\frac5{24})\); е) \((1\frac2{15}-\frac{11}{15})\cdot(5\frac3{18}-4\frac1{27})\).

а) Сначала сложим дроби: \(\frac49+\frac5{12}=\frac{16}{36}+\frac{15}{36}=\frac{31}{36}\). Затем \(\frac{31}{36}\cdot\frac{18}{31}=\frac12\).

б) \(\frac{11}{15}-\frac9{20}=\frac{44}{60}-\frac{27}{60}=\frac{17}{60}\). Тогда \(\frac6{25}\cdot\frac{17}{60}=\frac{17}{250}\).

в) \(4-3\frac7{15}=4-\frac{52}{15}=\frac8{15}\). Поэтому \(\frac8{15}\cdot\frac58=\frac13\).

г) \(5-4\frac47=\frac{35}{7}-\frac{32}{7}=\frac37\); \(7\frac16-6\frac5{12}=\frac{43}{6}-\frac{77}{12}=\frac9{12}=\frac34\). Произведение: \(\frac37\cdot\frac34=\frac9{28}\).

д) \(1\frac1{24}-\frac5{12}=\frac{25}{24}-\frac{10}{24}=\frac58\); \(4\frac18-3\frac5{24}=\frac{99}{24}-\frac{77}{24}=\frac{11}{12}\). Произведение: \(\frac58\cdot\frac{11}{12}=\frac{55}{96}\).

е) \(1\frac2{15}-\frac{11}{15}=\frac{17}{15}-\frac{11}{15}=\frac25\); \(5\frac3{18}-4\frac1{27}=\frac{31}{6}-\frac{109}{27}=\frac{279-218}{54}=\frac{61}{54}\). Произведение: \(\frac25\cdot\frac{61}{54}=\frac{61}{135}\).

Ответ: а) \(\frac12\); б) \(\frac{17}{250}\); в) \(\frac13\); г) \(\frac9{28}\); д) \(\frac{55}{96}\); е) \(\frac{61}{135}\).