Упр.841 ГДЗ Зубарева Мордкович 6 класс ФГОС (Математика)

Задача

а) (3/5-19/25)•4 11/16-(1:1,5)•(-3 3/8);
б) (7/12+3/4) :(-8/27)+(2-3 2/5)•25/28;
в) 42/45 :(2/3+8/15)-1:(3-1 1/5);
г) 8/19•(1 7/8-3/4+3 5/8)+5/14 :(4/7+11/14-1 3/14).

Подробный ответ

а) Преобразуем смешанные числа и выполняем действия по порядку:

$$ \left(\frac{3}{5}-\frac{19}{25}\right)\cdot 4\frac{11}{16}-\left(1:1{,}5\right)\cdot\left(-3\frac{3}{8}\right) $$
$$ \frac{3}{5}-\frac{19}{25}=\frac{15}{25}-\frac{19}{25}=-\frac{4}{25}, \qquad 4\frac{11}{16}=\frac{75}{16} $$
$$ 1:1{,}5=1:\frac{3}{2}=\frac{2}{3}, \qquad -3\frac{3}{8}=-\frac{27}{8} $$
$$ -\frac{4}{25}\cdot\frac{75}{16}-\frac{2}{3}\cdot\left(-\frac{27}{8}\right) =-\frac{3}{4}+\frac{9}{4} =\frac{6}{4} =\frac{3}{2} =1{,}5 $$

б)

$$ \left(\frac{7}{12}+\frac{3}{4}\right):\left(-\frac{8}{27}\right)+\left(2-3\frac{2}{5}\right)\cdot\frac{25}{28} $$
$$ \frac{7}{12}+\frac{3}{4}=\frac{7}{12}+\frac{9}{12}=\frac{16}{12}=\frac{4}{3} $$
$$ \frac{4}{3}:\left(-\frac{8}{27}\right)=\frac{4}{3}\cdot\left(-\frac{27}{8}\right)=-\frac{9}{2} $$
$$ 2-3\frac{2}{5}=2-\frac{17}{5}=\frac{10}{5}-\frac{17}{5}=-\frac{7}{5} $$
$$ -\frac{7}{5}\cdot\frac{25}{28}=-\frac{5}{4} $$
$$ -\frac{9}{2}-\frac{5}{4}=-\frac{18}{4}-\frac{5}{4}=-\frac{23}{4}=-5\frac{3}{4} $$

в)

$$ \frac{42}{45}:\left(\frac{2}{3}+\frac{8}{15}\right)-1:\left(3-1\frac{1}{5}\right) $$
$$ \frac{2}{3}+\frac{8}{15}=\frac{10}{15}+\frac{8}{15}=\frac{18}{15}=\frac{6}{5} $$
$$ \frac{42}{45}:\frac{6}{5}=\frac{42}{45}\cdot\frac{5}{6}=\frac{7}{9} $$
$$ 3-1\frac{1}{5}=3-\frac{6}{5}=\frac{15}{5}-\frac{6}{5}=\frac{9}{5} $$
$$ 1:\frac{9}{5}=\frac{5}{9} $$
$$ \frac{7}{9}-\frac{5}{9}=\frac{2}{9} $$

г)

$$ \frac{8}{19}\cdot\left(1\frac{7}{8}-\frac{3}{4}+3\frac{5}{8}\right)+\frac{5}{14}:\left(\frac{4}{7}+\frac{11}{14}-1\frac{3}{14}\right) $$
$$ 1\frac{7}{8}-\frac{3}{4}+3\frac{5}{8} =\frac{15}{8}-\frac{6}{8}+\frac{29}{8} =\frac{38}{8} =\frac{19}{4} $$
$$ \frac{8}{19}\cdot\frac{19}{4}=2 $$
$$ \frac{4}{7}+\frac{11}{14}-1\frac{3}{14} =\frac{8}{14}+\frac{11}{14}-\frac{17}{14} =\frac{2}{14} =\frac{1}{7} $$
$$ \frac{5}{14}:\frac{1}{7}=\frac{5}{14}\cdot 7=\frac{5}{2} $$
$$ 2+\frac{5}{2}=\frac{9}{2}=4{,}5 $$