Упр.450 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) 3*3/4: 3/8:1*3/7;
2) 3*3/4:( 3/8:1*3/7);
3) 1*7/9* 15/32:1*19/36;
4) 1*7/9*(15/32:1*19/36);
5) 3*4/7:1*1/7* 2/3;
6) 3*4/7:(1*1/7* 2/3);
7) (5/12+ 1/8): 3/8;
8) 5/12+ 1/8: 3/8;
9) 2*6/7:(5/6? 9/14);
10) 2*6/7: 5/6? 9/14;
11) 2*1/4:1*4/11? 3/8: 7/8;
12) (3*1/6?5*1/6:4*2/15)* 3/92.

1) $$3\frac{3}{4} : \frac{3}{8} : 1\frac{3}{7}$$

$$ 3\frac{3}{4}=\frac{15}{4}, \quad 1\frac{3}{7}=\frac{10}{7} $$
$$ \frac{15}{4}:\frac{3}{8}:\frac{10}{7} = \frac{15}{4}\cdot\frac{8}{3}\cdot\frac{7}{10} =7 $$

2) $$3\frac{3}{4} : \left(\frac{3}{8} : 1\frac{3}{7}\right)$$

$$ \frac{3}{8}:\frac{10}{7}=\frac{3}{8}\cdot\frac{7}{10}=\frac{21}{80} $$
$$ \frac{15}{4}:\frac{21}{80}=\frac{15}{4}\cdot\frac{80}{21}=14\frac{2}{7} $$

3) $$1\frac{7}{9}\cdot\frac{15}{32}:1\frac{19}{36}$$

$$ 1\frac{7}{9}=\frac{16}{9}, \quad 1\frac{19}{36}=\frac{55}{36} $$
$$ \frac{16}{9}\cdot\frac{15}{32}:\frac{55}{36} = \frac{16}{9}\cdot\frac{15}{32}\cdot\frac{36}{55} =\frac{6}{11} $$

4) $$1\frac{7}{9}\cdot\left(\frac{15}{32}:1\frac{19}{36}\right)$$

$$ \frac{15}{32}:\frac{55}{36}=\frac{15}{32}\cdot\frac{36}{55} $$
$$ \frac{16}{9}\cdot\frac{15}{32}\cdot\frac{36}{55} =\frac{6}{11} $$

5) $$3\frac{4}{7}:1\frac{1}{7}\cdot\frac{2}{3}$$

$$ 3\frac{4}{7}=\frac{25}{7}, \quad 1\frac{1}{7}=\frac{8}{7} $$
$$ \frac{25}{7}:\frac{8}{7}\cdot\frac{2}{3} = \frac{25}{7}\cdot\frac{7}{8}\cdot\frac{2}{3} =\frac{25}{12}=2\frac{1}{12} $$

6) $$3\frac{4}{7}:\left(1\frac{1}{7}\cdot\frac{2}{3}\right)$$

$$ \frac{25}{7}:\left(\frac{8}{7}\cdot\frac{2}{3}\right) = \frac{25}{7}:\frac{16}{21} = \frac{25}{7}\cdot\frac{21}{16} =\frac{75}{16}=4\frac{11}{16} $$

7) $$\left(\frac{5}{12}+\frac{1}{8}\right):\frac{3}{8}$$

$$ \frac{5}{12}+\frac{1}{8}=\frac{10}{24}+\frac{3}{24}=\frac{13}{24} $$
$$ \frac{13}{24}:\frac{3}{8}=\frac{13}{24}\cdot\frac{8}{3}=\frac{13}{9}=1\frac{4}{9} $$

8) $$\frac{5}{12}+\frac{1}{8}:\frac{3}{8}$$

$$ \frac{1}{8}:\frac{3}{8}=\frac{1}{8}\cdot\frac{8}{3}=\frac{1}{3} $$
$$ \frac{5}{12}+\frac{1}{3}=\frac{5}{12}+\frac{4}{12}=\frac{9}{12}=\frac{3}{4} $$

9) $$2\frac{6}{7}:\left(\frac{5}{6}-\frac{9}{14}\right)$$

$$ 2\frac{6}{7}=\frac{20}{7} $$
$$ \frac{5}{6}-\frac{9}{14}=\frac{35}{42}-\frac{27}{42}=\frac{8}{42}=\frac{4}{21} $$
$$ \frac{20}{7}:\frac{4}{21}=\frac{20}{7}\cdot\frac{21}{4}=15 $$

10) $$2\frac{6}{7}:\frac{5}{6}-\frac{9}{14}$$

$$ \frac{20}{7}:\frac{5}{6}-\frac{9}{14} = \frac{20}{7}\cdot\frac{6}{5}-\frac{9}{14} = \frac{24}{7}-\frac{9}{14} = \frac{48}{14}-\frac{9}{14} = \frac{39}{14} = 2\frac{11}{14} $$

11) $$2\frac{1}{4}:1\frac{4}{11}-\frac{3}{8}:\frac{7}{8}$$

$$ 2\frac{1}{4}=\frac{9}{4}, \quad 1\frac{4}{11}=\frac{15}{11} $$
$$ \frac{9}{4}:\frac{15}{11}=\frac{9}{4}\cdot\frac{11}{15}=\frac{33}{20} $$
$$ \frac{3}{8}:\frac{7}{8}=\frac{3}{8}\cdot\frac{8}{7}=\frac{3}{7} $$
$$ \frac{33}{20}-\frac{3}{7}=\frac{231}{140}-\frac{60}{140}=\frac{171}{140}=1\frac{31}{140} $$

12) $$\left(3\frac{1}{6}-5\frac{1}{6}:4\frac{2}{15}\right)\cdot\frac{3}{92}$$

$$ 3\frac{1}{6}=\frac{19}{6}, \quad 5\frac{1}{6}=\frac{31}{6}, \quad 4\frac{2}{15}=\frac{62}{15} $$
$$ \frac{31}{6}:\frac{62}{15}=\frac{31}{6}\cdot\frac{15}{62}=\frac{5}{4} $$
$$ \frac{19}{6}-\frac{5}{4}=\frac{38}{12}-\frac{15}{12}=\frac{23}{12} $$
$$ \frac{23}{12}\cdot\frac{3}{92}=\frac{23}{4\cdot 92}=\frac{1}{16} $$

Ответ

1) $$7$$; 2) $$14\frac{2}{7}$$; 3) $$\frac{6}{11}$$; 4) $$\frac{6}{11}$$; 5) $$2\frac{1}{12}$$; 6) $$4\frac{11}{16}$$; 7) $$1\frac{4}{9}$$; 8) $$\frac{3}{4}$$; 9) $$15$$; 10) $$2\frac{11}{14}$$; 11) $$1\frac{31}{140}$$; 12) $$\frac{1}{16}$$.