Упр.459 Часть 1 ГДЗ Виленкин Жохов 6 класс (Математика)

а) 4 11/18 * 6/7 — 1 4/9;
б) (1 1/2)3 — 2 1/4 * 1 1/3;
в) ((1 1/4)2 — 5/8) * 10 2/3 — 7 1/3;
г) (1 4/9 + 2 5/6 — 2 3/4) * (2 1/2 — 11/14).

а) Преобразуем смешанные числа в неправильные дроби:

$$4\frac{11}{18}\cdot\frac{6}{7}-1\frac{4}{9} =\frac{83}{18}\cdot\frac{6}{7}-1\frac{4}{9} =\frac{83\cdot 6}{18\cdot 7}-1\frac{4}{9} =\frac{83}{21}-1\frac{4}{9}$$

$$\frac{83}{21}=3\frac{20}{21},\qquad 1\frac{4}{9}=1\frac{28}{63},\qquad 3\frac{20}{21}=3\frac{60}{63}$$

$$3\frac{60}{63}-1\frac{28}{63}=2\frac{32}{63}$$

б)

$$\left(1\frac{1}{2}\right)^3-2\frac{1}{4}\cdot 1\frac{1}{3} =\left(\frac{3}{2}\right)^3-\frac{9}{4}\cdot\frac{4}{3} =\frac{27}{8}-3 =3\frac{3}{8}-3 =\frac{3}{8}$$

в)

$$\left(\left(1\frac{1}{4}\right)^2-\frac{5}{8}\right)\cdot 10\frac{2}{3}-7\frac{1}{3}$$

$$=\left(\left(\frac{5}{4}\right)^2-\frac{5}{8}\right)\cdot\frac{32}{3}-7\frac{1}{3} =\left(\frac{25}{16}-\frac{5}{8}\right)\cdot\frac{32}{3}-7\frac{1}{3}$$

$$=\left(\frac{25}{16}-\frac{10}{16}\right)\cdot\frac{32}{3}-7\frac{1}{3} =\frac{15}{16}\cdot\frac{32}{3}-7\frac{1}{3}$$

$$=5\cdot 2-7\frac{1}{3} =10-7\frac{1}{3} =9\frac{3}{3}-7\frac{1}{3} =2\frac{2}{3}$$

г)

$$\left(1\frac{4}{9}+2\frac{5}{6}-2\frac{3}{4}\right)\cdot\left(2\frac{1}{2}-\frac{11}{14}\right)$$

$$=\left(1\frac{16}{36}+2\frac{30}{36}-2\frac{27}{36}\right)\cdot\left(2\frac{7}{14}-\frac{11}{14}\right)$$

$$=\left(3\frac{46}{36}-2\frac{27}{36}\right)\cdot\left(1\frac{21}{14}-\frac{11}{14}\right) =1\frac{19}{36}\cdot 1\frac{10}{14}$$

$$=\frac{55}{36}\cdot\frac{24}{14} =\frac{55\cdot 24}{36\cdot 14} =\frac{55\cdot 2}{3\cdot 14} =\frac{55}{21} =2\frac{13}{21}$$

Ответ

а) $$2\frac{32}{63}$$; б) $$\frac{3}{8}$$; в) $$2\frac{2}{3}$$; г) $$2\frac{13}{21}$$.