Упр.184 Часть 1 ГДЗ Дорофеев Петерсон 6 класс (Математика)

Задача

1) (16 2/3-15 1/6+1,3)/(2,5•0,56•0,4);
2) (21,75-18 3/8)/(1,8:0,4•0,3);
3) ((2 5/6+1,75)•0,14)/(2 1/3•1,1:1,6);
4) ((2,1/0,4+3,3/1,8) :0,51•0,36)/(2 2/3•(4,5/4,2-1,6/2,8) );
5) (0,3•7,8:0,39-5/12•3,6)/(1 5/13•0,26:0,1+0,4);
6) ((2,4·3 1/4+7,1•3 1/4)•4/13)/((11/40-0,125)•6 1/3+17,1•0,5).

Подробный ответ

1) $$\frac{16\frac{2}{3}-15\frac{1}{6}+1,3}{2,5\cdot 0,56\cdot 0,4}$$

$$16\frac{2}{3}=16\frac{4}{6},\quad 1,3=1\frac{3}{10}$$
$$16\frac{4}{6}-15\frac{1}{6}=1\frac{3}{6}=1\frac{1}{2}$$
$$1\frac{1}{2}+1\frac{3}{10}=2\frac{8}{10}=2,8$$
$$2,5\cdot 0,56\cdot 0,4=0,56$$
$$2,8:0,56=5$$

2) $$\frac{21,75-18\frac{3}{8}}{1,8:0,4\cdot 0,3}$$

$$21,75=21\frac{3}{4}$$
$$21\frac{3}{4}-18\frac{3}{8}=3\frac{3}{8}$$
$$1,8:0,4\cdot 0,3=1,8: \frac{4}{10}\cdot \frac{3}{10}=1,8\cdot \frac{3}{4}\cdot \frac{3}{10}=0,54$$
$$3\frac{3}{8}:0,54=\frac{27}{8}:\frac{27}{50}=\frac{27}{8}\cdot \frac{50}{27}=\frac{25}{4}=6,25$$

3) $$\frac{\left(2\frac{5}{6}+1,75\right)\cdot 0,14}{2\frac{1}{3}\cdot 1,1:1,6}$$

$$2\frac{5}{6}=2\frac{10}{12},\quad 1,75=1\frac{3}{4}$$
$$2\frac{5}{6}+1,75=4\frac{7}{12}$$
$$4\frac{7}{12}\cdot 0,14=\frac{55}{12}\cdot \frac{14}{100}=\frac{77}{120}$$
$$2\frac{1}{3}\cdot 1,1:1,6=\frac{7}{3}\cdot \frac{11}{10}:\frac{8}{5}=\frac{77}{30}\cdot \frac{5}{8}=\frac{77}{48}$$
$$\frac{77}{120}:\frac{77}{48}=\frac{77}{120}\cdot \frac{48}{77}=\frac{2}{5}=0,4$$

4) $$\frac{\left(2,1:0,4+3,3:1,8\right):0,51\cdot 0,36}{2\frac{2}{3}\cdot \left(4,5:4,2-1,6:2,8\right)}$$

$$2,1:0,4=5,25,\quad 3,3:1,8=\frac{11}{6}$$
$$5,25+\frac{11}{6}=\frac{85}{12}$$
$$\frac{85}{12}:0,51\cdot 0,36=\frac{85}{12}:\frac{51}{100}\cdot \frac{36}{100}=\frac{17}{4}\cdot \frac{3}{100}=\frac{51}{400}$$
$$4,5:4,2-1,6:2,8=\frac{45}{42}-\frac{16}{28}=\frac{15}{14}-\frac{4}{7}=\frac{1}{2}$$
$$2\frac{2}{3}\cdot \frac{1}{2}=\frac{8}{3}\cdot \frac{1}{2}=\frac{4}{3}$$
$$\frac{51}{400}:\frac{4}{3}=\frac{51}{400}\cdot \frac{3}{4}=\frac{153}{1600}=0,095625$$

5) $$\frac{0,3\cdot 7,8:0,39-\frac{5}{12}\cdot 3,6}{1\frac{5}{13}\cdot 0,26:0,1+0,4}$$

$$0,3\cdot 7,8:0,39=0,3\cdot 20=6$$
$$\frac{5}{12}\cdot 3,6=\frac{5}{12}\cdot \frac{36}{10}=1,5$$
$$6-1,5=4,5$$
$$1\frac{5}{13}\cdot 0,26:0,1+0,4=\frac{18}{13}\cdot \frac{26}{100}:\frac{1}{10}+0,4=3,6+0,4=4$$
$$4,5:4=\frac{45}{40}=\frac{9}{8}=1,125$$

6) $$\frac{\left(2,4\cdot 3\frac{1}{4}+7,1\cdot 3\frac{1}{4}\right)\cdot \frac{4}{13}}{\left(\frac{11}{40}-0,125\right)\cdot 6\frac{1}{3}+17,1\cdot 0,5}$$

$$3\frac{1}{4}=\frac{13}{4},\quad 2,4+7,1=9,5$$
$$\left(2,4\cdot 3\frac{1}{4}+7,1\cdot 3\frac{1}{4}\right)\cdot \frac{4}{13}=3\frac{1}{4}\cdot 9,5\cdot \frac{4}{13}=9,5$$
$$0,125=\frac{1}{8},\quad \frac{11}{40}-\frac{1}{8}=\frac{11}{40}-\frac{5}{40}=\frac{3}{20}$$
$$6\frac{1}{3}=\frac{19}{3},\quad 17,1\cdot 0,5=\frac{171}{10}\cdot \frac{1}{2}=\frac{171}{20}$$
$$\frac{3}{20}\cdot \frac{19}{3}+\frac{171}{20}=\frac{19}{20}+\frac{171}{20}=\frac{190}{20}=9,5$$
$$9,5:9,5=1$$