Задание 20. Вычислите: а) (4/9 + 5/12) · 18/31; б) 6/25 · (11/15 − 9/20); в) (4 − 3 7/15) · 5/8; г) (1 1/24 − 5/12) · 4 1/8.

а) \(\left(\frac49+\frac5{12}\right)\cdot\frac{18}{31}=\left(\frac{16}{36}+\frac{15}{36}\right)\cdot\frac{18}{31}=\frac{31}{36}\cdot\frac{18}{31}=\frac12\).

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

в) \(\left(4-3\frac7{15}\right)\cdot\frac58=\frac8{15}\cdot\frac58=\frac13\).

г) \(\left(1\frac1{24}-\frac5{12}\right)\cdot4\frac18=\left(\frac{25}{24}-\frac{10}{24}\right)\cdot\frac{33}{8}=\frac58\cdot\frac{33}{8}=\frac{165}{64}=2\frac{37}{64}\).

Ответ: а) \(\frac12\); б) \(\frac{17}{250}\); в) \(\frac13\); г) \(2\frac{37}{64}\).