Контрольные задания
Вопрос:Фото задания: 1. Найдите значение выражения: 1) 4 1/7 · 14 − 2 1/4 · 3 1/6 − 1 1/9 · 3 3/8; 2) 1 31/32 · 3 1/5 − (8 5/9 · 6/35 + 2 2/15)…Фото задания

Ответ:

  1. Преобразуем смешанные числа в неправильные дроби:

    \(4\frac{1}{7}=\frac{29}{7}\), \(2\frac{1}{4}=\frac{9}{4}\), \(3\frac{1}{6}=\frac{19}{6}\), \(1\frac{1}{9}=\frac{10}{9}\), \(3\frac{3}{8}=\frac{27}{8}\).

    \(\frac{29}{7}\cdot14-\frac94\cdot\frac{19}{6}-\frac{10}{9}\cdot\frac{27}{8}=58-\frac{57}{8}-\frac{15}{4}=\frac{377}{8}=47\frac18\).

  2. \(1\frac{31}{32}=\frac{63}{32}\), \(3\frac15=\frac{16}{5}\), \(8\frac59=\frac{77}{9}\), \(2\frac{2}{15}=\frac{32}{15}\).

    \(\frac{63}{32}\cdot\frac{16}{5}-\left(\frac{77}{9}\cdot\frac{6}{35}+\frac{32}{15}\right)\cdot\frac{5}{12}\)

    \(=\frac{63}{10}-\left(\frac{22}{15}+\frac{32}{15}\right)\cdot\frac{5}{12}=\frac{63}{10}-\frac{18}{5}\cdot\frac{5}{12}=\frac{63}{10}-\frac32=\frac{24}{5}=4\frac45\).

  3. \(4\frac{5}{12}=\frac{101}{24}\), \(8\frac{13}{24}=\frac{205}{24}\), \(1\frac34=\frac74\).

    \(\left(\frac{101}{24}-\frac{205}{24}\right):\frac74+\frac56:\frac57\)

    \(=-\frac{13}{3}\cdot\frac47+\frac56\cdot\frac75=-\frac{52}{21}+\frac76=-\frac{55}{42}\).

  4. \(2,06:\frac1{60}=123\), \(14,84:\frac7{60}=127,2\).

    \((123-127,2)\cdot\frac16-0,084:\frac1{12}=(-4,2)\cdot\frac16-1,008=-0,7-1,008=-1,708\).

  5. \((-16,2:32,4-21,2:(-10,6))\cdot(-2,8) =(-0,5-(-2))\cdot(-2,8)=1,5\cdot(-2,8)=-4,2\).

  6. \((-2,3-3,91:(-2,3)):(-0,01)\cdot(-0,7) =(-2,3-(-1,7)):(-0,01)\cdot(-0,7) =(-0,6):(-0,01)\cdot(-0,7)=60\cdot(-0,7)=-42\).

  7. \(\left(-\frac{11}{15}-\frac7{20}\right):\left(-3\frac14\right) =\left(-\frac{44}{60}-\frac{21}{60}\right):\left(-\frac{13}{4}\right) =-\frac{13}{12}\cdot\left(-\frac4{13}\right)=\frac13\).

Ответ: 1) \(47\frac18\); 2) \(4\frac45\); 3) \(-\frac{55}{42}\); 4) \(-1,708\); 5) \(-4,2\); 6) \(-42\); 7) \(\frac13\).