Вопрос:

а) \(\frac{1}{4}-(1-\frac{11}{12})\); б) \(2-(\frac{13}{33}-\frac{5}{22})\); в) \(6\frac{3}{16}-(2\frac{3}{8}+3\frac{5}{12})\); г) \(8\frac{1}{12}-3\frac{4}{15}-1\frac{7}{30}\); д) \((13-8\frac{5}{12})+(17\frac{1}{2}-16\frac{1}{5})\); е) \((63\frac{2}{3}+3\frac{1}{8})-(13-10\frac{5}{9})\); ж) \((15\frac{1}{2}-2\frac{3}{8})-(5\frac{5}{6}+6\frac{3}{4})+(10\frac{2}{3}-5\frac{5}{8})\).

Ответ:

  1. \[\frac14-\left(1-\frac{11}{12}\right)=\frac14-\frac1{12}=\frac3{12}-\frac1{12}=\frac16.\]
  2. \[2-\left(\frac{13}{33}-\frac5{22}\right)=2-\left(\frac{26}{66}-\frac{15}{66}\right)=2-\frac{11}{66}=2-\frac16=1\frac56.\]
  3. \[6\frac3{16}-\left(2\frac38+3\frac5{12}\right)=6\frac3{16}-5\frac{19}{24}.\] \[6\frac3{16}=6\frac9{48},\quad 5\frac{19}{24}=5\frac{38}{48};\quad 6\frac9{48}-5\frac{38}{48}=\frac{287}{48}-\frac{278}{48}=\frac9{48}=\frac3{16}.\]
  4. \[8\frac1{12}-3\frac4{15}-1\frac7{30}=\frac{243}{30}-\frac{102}{30}-\frac{37}{30}=\frac{104}{30}=3\frac7{15}.\]
  5. \[(13-8\frac5{12})+(17\frac12-16\frac15)=4\frac7{12}+1\frac3{10}=5\frac{53}{60}.\]
  6. \[(63\frac23+3\frac18)-(13-10\frac59)=66\frac{19}{24}-2\frac49=64\frac{11}{24}.\]
  7. \[(15\frac12-2\frac38)-(5\frac56+6\frac34)+(10\frac23-5\frac58)\] \[=13\frac18-12\frac7{12}+5\frac1{24}=5\frac{15}{24}=5\frac58.\]

Ответ: а) \(\frac16\); б) \(1\frac56\); в) \(\frac3{16}\); г) \(3\frac7{15}\); д) \(5\frac{53}{60}\); е) \(64\frac{11}{24}\); ж) \(5\frac58\).