Упр.241 Часть 2 ГДЗ Виленкин Жохов 6 класс (Математика)

Задача

а) (2 7/15 — 4) * (8 16/23 — 10);
б) 11 1/4 * 1/9 — 4 7/12 * 4/11;
в) 22,5 — 24 * (2/9 — 2/3);
г) (-3/7 — 5/14 — 8/21) * 3/14 + 1/8;
д) (4 1/3 — 2,2) * (-3/16) — 3,05;
е) (-0,25 — 3/4 — 1/2) * (-0,2) + 3,9.

Подробный ответ

а) Преобразуем смешанные числа в неправильные дроби:

$$ \left(2\frac{7}{15}-4\right)\cdot\left(8\frac{16}{23}-10\right) = \left(-3\frac{8}{15}\right)\cdot\left(-1\frac{7}{23}\right) $$
$$ = \left(-\frac{53}{15}\right)\cdot\left(-\frac{30}{23}\right) = \frac{53}{15}\cdot\frac{30}{23} = \frac{53\cdot 2}{23} = \frac{106}{23} = 2 $$

б)

$$ 11\frac{1}{4}\cdot\frac{1}{9}-4\frac{7}{12}\cdot\frac{4}{11} = \frac{45}{4}\cdot\frac{1}{9}-\frac{55}{12}\cdot\frac{4}{11} $$
$$ = \frac{5}{4}-\frac{5}{3} = \frac{15}{12}-\frac{20}{12} = -\frac{5}{12} $$

в)

$$ 22{,}5-24\cdot\left(\frac{2}{9}-\frac{2}{3}\right) = 22{,}5-24\cdot\left(\frac{2}{9}-\frac{6}{9}\right) $$
$$ = 22{,}5-24\cdot\left(-\frac{4}{9}\right) = 22{,}5+\frac{96}{9} = 22{,}5+10\frac{2}{3} $$
$$ = 22\frac{1}{2}+10\frac{2}{3} = 33\frac{1}{6} $$

г)

$$ \left(-\frac{3}{7}-\frac{5}{14}-\frac{8}{21}\right)\cdot\frac{3}{14}+\frac{1}{8} $$
$$ = \left(-\frac{18}{42}-\frac{15}{42}-\frac{16}{42}\right)\cdot\frac{3}{14}+\frac{1}{8} = \left(-\frac{49}{42}\right)\cdot\frac{3}{14}+\frac{1}{8} $$
$$ = -\frac{7}{6}\cdot\frac{3}{14}+\frac{1}{8} = -\frac{1}{4}+\frac{1}{8} = -\frac{1}{8} $$

д)

$$ \left(4\frac{1}{3}-2{,}2\right)\cdot\left(-\frac{3}{16}\right)-3{,}05 = \left(4\frac{1}{3}-2\frac{1}{5}\right)\cdot\left(-\frac{3}{16}\right)-3{,}05 $$
$$ = \left(4\frac{5}{15}-2\frac{3}{15}\right)\cdot\left(-\frac{3}{16}\right)-3{,}05 = 2\frac{2}{15}\cdot\left(-\frac{3}{16}\right)-3{,}05 $$
$$ = -\frac{32}{15}\cdot\frac{3}{16}-3{,}05 = -\frac{2}{5}-3{,}05 = -3{,}45 $$

е)

$$ \left(-0{,}25-\frac{3}{4}-\frac{1}{2}\right)\cdot(-0{,}2)+3{,}9 = \left(-0{,}25-0{,}75-0{,}5\right)\cdot(-0{,}2)+3{,}9 $$
$$ = (-1{,}5)\cdot(-0{,}2)+3{,}9 = 0{,}3+3{,}9 = 4{,}2 $$