Упр.352 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) 4*2/3*6?1*23/42*3*1/13+2*1/8*1*29/51 ;
2) (5*3/10?3*4/5*13/38)* 5/84+2*1/12* 4/15 ;
3) (3*1/3)2?2*13/16*2*2/5 ;
4) (5/12+ 13/20)2*1*13/32.

1) $$4\frac{2}{3}\cdot 6-1\frac{23}{42}\cdot 3\frac{1}{13}+2\frac{1}{8}\cdot 1\frac{29}{51}$$

Преобразуем смешанные числа в неправильные дроби:

$$4\frac{2}{3}=\frac{14}{3},\quad 1\frac{23}{42}=\frac{65}{42},\quad 3\frac{1}{13}=\frac{40}{13},\quad 2\frac{1}{8}=\frac{17}{8},\quad 1\frac{29}{51}=\frac{80}{51}$$

$$\frac{14}{3}\cdot 6-\frac{65}{42}\cdot \frac{40}{13}+\frac{17}{8}\cdot \frac{80}{51}$$

$$28-\frac{100}{21}+\frac{10}{3}$$

$$28-\frac{100}{21}+3\frac{1}{3}$$

$$28-4\frac{16}{21}+3\frac{7}{21}=23\frac{5}{21}+3\frac{7}{21}=26\frac{12}{21}=26\frac{4}{7}$$

2) $$\left(5\frac{3}{10}-3\frac{4}{5}\cdot \frac{13}{38}\right)\cdot \frac{5}{84}+2\frac{1}{12}\cdot \frac{4}{15}$$

$$3\frac{4}{5}=\frac{19}{5},\quad 5\frac{3}{10}=\frac{53}{10},\quad 2\frac{1}{12}=\frac{25}{12}$$

$$\left(\frac{53}{10}-\frac{19}{5}\cdot \frac{13}{38}\right)\cdot \frac{5}{84}+\frac{25}{12}\cdot \frac{4}{15}$$

$$\left(\frac{53}{10}-\frac{13}{10}\right)\cdot \frac{5}{84}+\frac{5}{9}$$

$$4\cdot \frac{5}{84}+\frac{5}{9}=\frac{5}{21}+\frac{5}{9}$$

$$\frac{15}{63}+\frac{35}{63}=\frac{50}{63}$$

3) $$\left(3\frac{1}{3}\right)^2-2\frac{13}{16}\cdot 2\frac{2}{5}$$

$$3\frac{1}{3}=\frac{10}{3},\quad 2\frac{13}{16}=\frac{45}{16},\quad 2\frac{2}{5}=\frac{12}{5}$$

$$\left(\frac{10}{3}\right)^2-\frac{45}{16}\cdot \frac{12}{5}$$

$$\frac{100}{9}-\frac{9}{4}\cdot 3$$

$$11\frac{1}{9}-6\frac{3}{4}=11\frac{4}{36}-6\frac{27}{36}=4\frac{13}{36}$$

4) $$\left(\frac{5}{12}+\frac{13}{20}\right)^2\cdot 1\frac{13}{32}$$

$$\frac{5}{12}+\frac{13}{20}=\frac{25}{60}+\frac{39}{60}=\frac{64}{60}=\frac{16}{15}$$

$$\left(\frac{16}{15}\right)^2\cdot \frac{45}{32}=\frac{256}{225}\cdot \frac{45}{32}$$

$$\frac{8}{5}=1\frac{3}{5}$$

Ответ

1) $$26\frac{4}{7}$$; 2) $$\frac{50}{63}$$; 3) $$4\frac{13}{36}$$; 4) $$1\frac{3}{5}$$.