Упр.342 ГДЗ Мерзляк Полонский 6 класс (Математика)

Задача

1) 15*4/9?4 4/9*3*3/8 ;
2) 81/88*(6?1*13/15*1*19/21) ;
3) (5*1/16?1*1/8)*(5/6+ 3/14) ;
4) 5*1/16?1*1/8*(5/6+ 3/14).

Подробный ответ

1) $$15\frac{4}{9}-4\frac{4}{9}\cdot 3\frac{3}{8}$$

$$15\frac{4}{9}-4\frac{4}{9}\cdot 3\frac{3}{8}=15\frac{4}{9}-\frac{40}{9}\cdot\frac{27}{8}=15\frac{4}{9}-5\cdot 3=15\frac{4}{9}-15=\frac{4}{9}.$$

2) $$\frac{81}{88}\left(6-1\frac{13}{15}\cdot 1\frac{19}{21}\right)$$

$$\frac{81}{88}\left(6-1\frac{13}{15}\cdot 1\frac{19}{21}\right)=\frac{81}{88}\left(6-\frac{28}{15}\cdot\frac{40}{21}\right)=\frac{81}{88}\left(6-\frac{4\cdot 8}{3\cdot 3}\right)$$
$$=\frac{81}{88}\left(6-\frac{32}{9}\right)=\frac{81}{88}\left(5\frac{9}{9}-3\frac{5}{9}\right)=\frac{81}{88}\cdot 2\frac{4}{9}=\frac{81}{88}\cdot\frac{22}{9}=\frac{9}{4}=2\frac{1}{4}.$$

3) $$\left(5\frac{1}{16}-1\frac{1}{8}\right)\left(\frac{5}{6}+\frac{3}{14}\right)$$

$$\left(5\frac{1}{16}-1\frac{1}{8}\right)\left(\frac{5}{6}+\frac{3}{14}\right)=\left(4\frac{17}{16}-1\frac{2}{16}\right)\left(\frac{35}{42}+\frac{9}{42}\right)$$
$$=3\frac{15}{16}\cdot\frac{44}{42}=\frac{63}{16}\cdot\frac{22}{21}=\frac{63\cdot 22}{16\cdot 21}=\frac{3\cdot 11}{8\cdot 1}=\frac{33}{8}=4\frac{1}{8}.$$

4) $$5\frac{1}{16}-1\frac{1}{8}\left(\frac{5}{6}+\frac{3}{14}\right)$$

$$5\frac{1}{16}-1\frac{1}{8}\left(\frac{5}{6}+\frac{3}{14}\right)=5\frac{1}{16}-\frac{9}{8}\cdot\frac{44}{42}$$
$$=5\frac{1}{16}-\frac{9\cdot 22}{8\cdot 21}=5\frac{1}{16}-\frac{3\cdot 11}{4\cdot 7}=5\frac{1}{16}-\frac{33}{28}$$
$$=5\frac{1}{16}-1\frac{5}{28}=5\frac{7}{112}-1\frac{20}{112}=3\frac{99}{112}.$$