Упр.2.399 ГДЗ Виленкин Жохов 6 класс Часть 1, Просвещение (Математика)

а) $$\frac{4}{7}x+\frac{5}{14}x=\left(\frac{4}{7}+\frac{5}{14}\right)x=\left(\frac{8}{14}+\frac{5}{14}\right)x=\frac{13}{14}x.$$

При $$x=5\frac{1}{4}:$$

$$\frac{13}{14}x=\frac{13}{14}\cdot 5\frac{1}{4} =\frac{13}{14}\cdot \frac{21}{4} =\frac{13\cdot 21}{14\cdot 4} =\frac{13\cdot 3}{2\cdot 4} =\frac{39}{8} =4\frac{7}{8}.$$

При $$x=\frac{9}{13}:$$

$$\frac{13}{14}x=\frac{13}{14}\cdot \frac{9}{13} =\frac{9}{14}.$$

б) $$\frac{5}{16}y+y-\frac{3}{8}y=\left(\frac{5}{16}+1-\frac{3}{8}\right)y=\left(\frac{5}{16}+\frac{16}{16}-\frac{6}{16}\right)y=\frac{15}{16}y.$$

При $$y=1\frac{1}{15}:$$

$$\frac{15}{16}y=\frac{15}{16}\cdot 1\frac{1}{15} =\frac{15}{16}\cdot \frac{16}{15} =1.$$

При $$y=1\frac{7}{8}:$$

$$\frac{15}{16}y=\frac{15}{16}\cdot 1\frac{7}{8} =\frac{15}{16}\cdot \frac{15}{8} =\frac{225}{128} =1\frac{97}{128}.$$

в) $$\frac{17}{42}c-\frac{2}{7}c+\frac{7}{18}c=\left(\frac{17}{42}-\frac{2}{7}+\frac{7}{18}\right)c=\left(\frac{51}{126}-\frac{36}{126}+\frac{49}{126}\right)c=\frac{64}{126}c=\frac{32}{63}c.$$

При $$c=3\frac{1}{2}:$$

$$\frac{32}{63}c=\frac{32}{63}\cdot 3\frac{1}{2} =\frac{32}{63}\cdot \frac{7}{2} =\frac{16}{9} =1\frac{7}{9}.$$

При $$c=2\frac{5}{8}:$$

$$\frac{32}{63}c=\frac{32}{63}\cdot 2\frac{5}{8} =\frac{32}{63}\cdot \frac{21}{8} =\frac{4}{3} =1\frac{1}{3}.$$

г) $$\frac{3}{4}n+\frac{2}{3}n-\frac{4}{18}n=\left(\frac{3}{4}+\frac{2}{3}-\frac{4}{18}\right)n=\left(\frac{27}{36}+\frac{24}{36}-\frac{8}{36}\right)n=\frac{43}{36}n.$$

При $$n=1\frac{13}{23}:$$

$$\frac{43}{36}n=\frac{43}{36}\cdot 1\frac{13}{23} =\frac{43}{36}\cdot \frac{36}{23} =\frac{43}{23} =1\frac{20}{23}.$$

При $$n=\frac{6}{41}:$$

$$\frac{43}{36}n=\frac{43}{36}\cdot \frac{6}{41} =\frac{43}{246}.$$

Ответ

а) $$4\frac{7}{8};\ \frac{9}{14}.$$
б) $$1;\ 1\frac{97}{128}.$$
в) $$1\frac{7}{9};\ 1\frac{1}{3}.$$
г) $$1\frac{20}{23};\ \frac{43}{246}.$$

а) $$4\frac{3}{5}n+m$$ при $$n=1\frac{4}{23},\ m=6\frac{13}{30}:$$

$$4\frac{3}{5}n+m =4\frac{3}{5}\cdot 1\frac{4}{23}+6\frac{13}{30} =\frac{23}{5}\cdot \frac{27}{23}+6\frac{13}{30} =\frac{27}{5}+6\frac{13}{30} =5\frac{2}{5}+6\frac{13}{30}$$

$$=5\frac{12}{30}+6\frac{13}{30} =(5+6)+\left(\frac{12}{30}+\frac{13}{30}\right) =11+\frac{25}{30} =11\frac{5}{6}.$$

б) $$5\frac{1}{7}(n+m)$$ при $$n=1\frac{7}{9},\ m=2\frac{1}{9}:$$

$$5\frac{1}{7}(n+m) =5\frac{1}{7}\left(1\frac{7}{9}+2\frac{1}{9}\right) =5\frac{1}{7}\left((1+2)+\left(\frac{7}{9}+\frac{1}{9}\right)\right) =5\frac{1}{7}\cdot 3\frac{8}{9}$$

$$=\frac{36}{7}\cdot \frac{35}{9} =\frac{36\cdot 35}{7\cdot 9} =\frac{4\cdot 9\cdot 5\cdot 7}{7\cdot 9} =20.$$

Ответ

а) $$11\frac{5}{6}.$$
б) $$20.$$