Упр.351 ГДЗ Мерзляк Полонский 6 класс (Математика)

Задача

1) 5*3/4*8?2*1/3*1 3/14?1 37/48*2*2/15 ;
2) 1*3/22*2*14/15?(1*5/8+2 1/8* 11/17)* 3/7 ;
3) 6*2/5*1*9/16?(2*1/4)2 ;
4) (2*7/10?1*8/15)2* 9/14.

Подробный ответ

1) Преобразуем смешанные числа в неправильные дроби и выполняем действия по порядку:

$$ 5\frac{3}{4}\cdot 8-2\frac{1}{3}\cdot 1\frac{3}{14}-1\frac{37}{48}\cdot 2\frac{2}{15} = \frac{23}{4}\cdot 8-\frac{7}{3}\cdot \frac{17}{14}-\frac{85}{48}\cdot \frac{32}{15} $$
$$ =46-\frac{17}{6}-\frac{34}{9} =46-2\frac{5}{6}-3\frac{7}{9} $$
$$ =45\frac{36}{36}-2\frac{30}{36}-3\frac{28}{36} =43\frac{6}{36}-3\frac{28}{36} =42\frac{42}{36}-3\frac{28}{36} =39\frac{14}{36} =39\frac{7}{18}. $$

2) Сначала вычислим выражение в скобках:

$$ 1\frac{3}{22}\cdot 2\frac{14}{15}-\left(1\frac{5}{8}+2\frac{1}{8}\cdot \frac{11}{17}\right)\cdot \frac{3}{7} = \frac{25}{22}\cdot \frac{44}{15}-\left(1\frac{5}{8}+\frac{17}{8}\cdot \frac{11}{17}\right)\cdot \frac{3}{7} $$
$$ =\frac{5}{1}\cdot \frac{2}{3}-\left(1\frac{5}{8}+\frac{11}{8}\right)\cdot \frac{3}{7} =\frac{10}{3}-\left(1\frac{5}{8}+1\frac{3}{8}\right)\cdot \frac{3}{7} $$
$$ =\frac{10}{3}-3\frac{1}{3}\cdot \frac{3}{7} =3\frac{1}{3}-\frac{9}{21} =3\frac{7}{21}-1\frac{2}{7} =3\frac{7}{21}-1\frac{6}{21} =2\frac{1}{21}. $$

3)

$$ 6\frac{2}{5}\cdot 1\frac{9}{16}-\left(2\frac{1}{4}\right)^2 = \frac{32}{5}\cdot \frac{25}{16}-\left(\frac{9}{4}\right)^2 $$
$$ =2\cdot 5-\frac{81}{16} =10-5\frac{1}{16} =9\frac{16}{16}-5\frac{1}{16} =4\frac{15}{16}. $$

4)

$$ \left(2\frac{7}{10}-1\frac{8}{15}\right)^2\cdot \frac{9}{14} = \left(2\frac{21}{30}-1\frac{16}{30}\right)^2\cdot \frac{9}{14} $$
$$ =\left(1\frac{5}{30}\right)^2\cdot \frac{9}{14} =\left(1\frac{1}{6}\right)^2\cdot \frac{9}{14} =\left(\frac{7}{6}\right)^2\cdot \frac{9}{14} $$
$$ =\frac{49}{36}\cdot \frac{9}{14} =\frac{7}{4}\cdot \frac{1}{2} =\frac{7}{8}. $$