1.038. Вычислите: ((3 7/12 − 2 11/18 + 2 1/24) · 1 5/31 − 3/52 · (3 1/2 + 5/6)) · 1 7/13 / (19/84 : (5 13/42 − 2 13/28 + 5/24) + 1 2/27 − 1/3 · 4/9).

\(3\frac7{12}-2\frac{11}{18}+2\frac1{24}=\frac{43}{12}-\frac{47}{18}+\frac{49}{24}=\frac{31}{72}\).

\(\frac{31}{72}\cdot\frac{36}{31}=\frac12\), а \(\frac3{52}\left(\frac72+\frac56\right)=\frac3{52}\cdot\frac{13}{3}=\frac14\).

Числитель: \((\frac12-\frac14)\cdot\frac{20}{13}=\frac5{13}\).

В знаменателе: \(5\frac{13}{42}-2\frac{13}{28}+\frac5{24}=\frac{89}{21}-\frac{69}{28}+\frac5{24}=\frac{19}{24}\), поэтому \(\frac{19}{84}:\frac{19}{24}=\frac27\). Кроме того, \(1\frac2{27}-\frac13\cdot\frac49=\frac{29}{27}-\frac4{27}=\frac{25}{27}\).

Знаменатель: \(\frac27+\frac{25}{27}=\frac{103}{189}\).

\(\frac5{13}:\frac{103}{189}=\frac{945}{1339}\).

Ответ: \(\frac{945}{1339}\).