Упр.360 ГДЗ Мерзляк Полонский 6 класс (Математика)

1. Упростите выражение и найдите его значение:
   
   1) $$\frac{3}{8}x+\frac{4}{9}x?\frac{5}{12}x$$, если $$x=3\frac{3}{29}$$;
   
   2) $$\frac{9}{10}c?\frac{2}{15}c?\frac{3}{5}c$$, если $$c=2{,}4$$;
   
   3) $$3*\frac{3}{5}y?2*\frac{1}{3}y?\frac{1}{15}y$$, если $$y=10$$.

1) При $$x=3\frac{3}{29}=\frac{90}{29}$$:

$$\frac{3}{8}x+\frac{4}{9}x-\frac{5}{12}x = \frac{27}{72}x+\frac{32}{72}x-\frac{30}{72}x = \frac{29}{72}x$$
$$\frac{29}{72}\cdot \frac{90}{29} = \frac{90}{72} = \frac{5}{4} = 1\frac{1}{4}$$

2) При $$c=2{,}4=\frac{24}{10}=\frac{12}{5}$$:

$$\frac{9}{10}c-\frac{2}{15}c-\frac{3}{5}c = \frac{27}{30}c-\frac{4}{30}c-\frac{18}{30}c = \frac{5}{30}c = \frac{1}{6}c$$
$$\frac{1}{6}\cdot \frac{12}{5} = \frac{2}{5}$$

3) При $$y=10$$:

$$3\frac{3}{5}y-2\frac{1}{3}y-\frac{1}{15}y = \frac{18}{5}y-\frac{7}{3}y-\frac{1}{15}y = \frac{54}{15}y-\frac{35}{15}y-\frac{1}{15}y = \frac{18}{15}y = \frac{6}{5}y$$
$$\frac{6}{5}\cdot 10=12$$

Ответ

1) $$1\frac{1}{4}$$; 2) $$\frac{2}{5}$$; 3) $$12$$.