Вычислите: \(\left(1\frac{11}{24}+\frac{13}{36}\right)\cdot1{,}44-\frac{8}{15}\cdot0{,}5625\).

Преобразуем числа в дроби: \(1\frac{11}{24}=\frac{35}{24}\), \(1{,}44=\frac{36}{25}\), \(0{,}5625=\frac{9}{16}\).

\[\left(\frac{35}{24}+\frac{13}{36}\right)\cdot\frac{36}{25}-\frac{8}{15}\cdot\frac{9}{16}\]

\[\frac{35}{24}+\frac{13}{36}=\frac{105}{72}+\frac{26}{72}=\frac{131}{72}\]

\[\frac{131}{72}\cdot\frac{36}{25}=\frac{131}{50},\qquad \frac{8}{15}\cdot\frac{9}{16}=\frac{3}{10}\]

\[\frac{131}{50}-\frac{3}{10}=\frac{131}{50}-\frac{15}{50}=\frac{116}{50}=\frac{58}{25}=2{,}32\]

Ответ: \(2{,}32\).