Вопрос:

Вычислите: а) 1/4 − (1 − 11/12); б) 2 − (13/33 − 5/22); в) 6 3/16 − (2 3/8 + 3 5/12); г) 8 1/12 − 3 4/15 − 1 7/30; д) (13 − 8 5/12) + (17 1/2 − 16 1/5); е) (63 2/3 + 3 1/8) − (13 − 10 5/9); ж) (15 1/2 − 2 3/8) − (5 5/6 + 6 3/4) + (10 2/3 − 5 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. \(6\frac3{16}-\left(2\frac38+3\frac5{12}\right)=6\frac3{16}-5\frac{19}{24}=\frac{99}{16}-\frac{139}{24}=\frac{297-278}{48}=\frac{19}{48}\).
  4. \(8\frac1{12}-3\frac4{15}-1\frac7{30}=\frac{485}{60}-\frac{196}{60}-\frac{37}{30}=\frac{485-196-74}{60}=\frac{215}{60}=3\frac7{12}\).
  5. \((13-8\frac5{12})+(17\frac12-16\frac15)=4\frac7{12}+1\frac3{10}=5\frac{29}{60}\).
  6. \((63\frac23+3\frac18)-(13-10\frac59)=65\frac{19}{24}-2\frac49=63\frac7{24}\).
  7. \((15\frac12-2\frac38)-(5\frac56+6\frac34)+(10\frac23-5\frac58)=13\frac18-12\frac7{12}+5\frac1{24}=5\frac{13}{24}\).

Ответ: а) \(\frac16\); б) \(1\frac56\); в) \(\frac{19}{48}\); г) \(3\frac7{12}\); д) \(5\frac{29}{60}\); е) \(63\frac7{24}\); ж) \(5\frac{13}{24}\).