Упр.758 ГДЗ Ткачёва 6 класс (Математика)

Задача

1) (5/8 — 11/12) · (-8/21); 2) 9/34 · (-5/18 — 1/27);
3) (-1 3/4)^2 : (1/2 — 7/8); 4) (1/6 — 11/18) · (-1 1/2)^3;
5) (-2/3)^3 + (5/7)^2 · (-7/15); 6) (-5/6)^2 — 1/18 : (-2/3)^3.

Подробный ответ

1) $$\left(\frac{5}{8}-\frac{11}{12}\right)\cdot\left(-\frac{8}{21}\right)=\left(\frac{15}{24}-\frac{22}{24}\right)\cdot\left(-\frac{8}{21}\right)=-\frac{7}{24}\cdot\left(-\frac{8}{21}\right)=\frac{7\cdot 8}{24\cdot 21}=\frac{1}{9}.$$

2) $$\frac{9}{34}\cdot\left(-\frac{5}{18}-\frac{1}{27}\right)=\frac{9}{34}\cdot\left(-\frac{15}{54}-\frac{2}{54}\right)=\frac{9}{34}\cdot\left(-\frac{17}{54}\right)=-\frac{9\cdot 17}{34\cdot 54}=-\frac{1}{12}.$$

3) $$\left(-1\frac{3}{4}\right)^2:\left(\frac{1}{2}-\frac{7}{8}\right)=\left(-\frac{7}{4}\right)^2:\left(\frac{4}{8}-\frac{7}{8}\right)=\frac{49}{16}:\left(-\frac{3}{8}\right)=\frac{49}{16}\cdot\left(-\frac{8}{3}\right)=-\frac{49}{6}=-8\frac{1}{6}.$$

4) $$\left(\frac{1}{6}-\frac{11}{18}\right)\cdot\left(-1\frac{1}{2}\right)^3=\left(\frac{3}{18}-\frac{11}{18}\right)\cdot\left(-\frac{3}{2}\right)^3=-\frac{8}{18}\cdot\left(-\frac{27}{8}\right)=\frac{3}{2}=1{,}5.$$

5) $$\left(-\frac{2}{3}\right)^3+\left(\frac{5}{7}\right)^2\cdot\left(-\frac{7}{15}\right)=-\frac{8}{27}+\frac{25}{49}\cdot\left(-\frac{7}{15}\right)=-\frac{8}{27}-\frac{25\cdot 7}{49\cdot 15}=-\frac{8}{27}-\frac{5}{21}=-\frac{56}{189}-\frac{45}{189}=-\frac{101}{189}.$$

6) $$\left(-\frac{5}{6}\right)^2-\frac{1}{18}:\left(-\frac{2}{3}\right)^3=\frac{25}{36}-\frac{1}{18}:\left(-\frac{8}{27}\right)=\frac{25}{36}+\frac{1}{18}\cdot\frac{27}{8}=\frac{25}{36}+\frac{3}{16}=\frac{100}{144}+\frac{27}{144}=\frac{127}{144}.$$