451. Найдите значение выражения: 1) 12:3$$\frac{3}{8}$$-1$$\frac{1}{4}$$\cdot$$2$$\frac{15}{32}; 2) 1$$\frac{31}{35}$$:(2$$\frac{8}{9}$$:1$$\frac{19}{45}$$); 3) (1$$\frac{1}{35}$$:$$\frac{4}{5}$$-1$$\frac{8}{35}$$) $$\cdot$$ 3$$\frac{1}{3}$$; 4) (7-1$$\frac{5}{9}$$:$$\frac{7}{24}$$) $$\cdot$$ 3$$\frac{20}{27}$$. 453. Решите уравнение: 1) $$\frac{25}{27}$$x = $$\frac{5}{18}$$; 2) $$\frac{13}{17}$$x = 39; 3) 4x = $$\frac{5}{7}$$; 4) x: 2$$\frac{2}{15}$$ = 1$$\frac{9}{16}$$; 5) 4$$\frac{4}{9}$$: x = $$\frac{5}{27}$$; 6) 1$$\frac{4}{9}$$x = 5,2. 464. Решите уравнение: 1) 2$$\frac{2}{11}$$x - $$\frac{5}{16}$$ = 1$$\frac{3}{4}$$; 2) 4$$\frac{2}{9}$$x + 3$$\frac{5}{14}$$ = 6$$\frac{11}{21}$$; 3) $$\frac{11}{18}$$ - $$\frac{14}{27}$$x = $$\frac{5}{12}$$; 4) $$\frac{1}{3}$$x + $$\frac{1}{4}$$x + $$\frac{1}{5}$$x = 1$$\frac{19}{75}$$; 5) 4$$\frac{1}{2}$$: x + 1$$\frac{3}{4}$$ = 3$$\frac{19}{28}$$; 6) 3$$\frac{2}{3}$$:(x - 2$$\frac{4}{15}$$) = 3$$\frac{5}{13}$$.

451. Найдите значение выражения:

1)

Давай решим по действиям:

1) 3$$\frac{3}{8}$$ = $$\frac{3 \times 8 + 3}{8}$$ = $$\frac{24+3}{8}$$ = $$\frac{27}{8};

2) 1$$\frac{1}{4}$$ = $$\frac{1 \times 4 + 1}{4}$$ = $$\frac{4+1}{4}$$ = $$\frac{5}{4};

3) 2$$\frac{15}{32}$$ = $$\frac{2 \times 32 + 15}{32}$$ = $$\frac{64+15}{32}$$ = $$\frac{79}{32};

4) 12 : $$\frac{27}{8}$$ = 12 $$\times$$ $$\frac{8}{27}$$ = $$\frac{12 \times 8}{27}$$ = $$\frac{96}{27}$$ = $$\frac{32}{9};

5) $$\frac{5}{4}$$ $$\times$$ $$\frac{79}{32}$$ = $$\frac{5 \times 79}{4 \times 32}$$ = $$\frac{395}{128};

6) $$\frac{32}{9}$$ - $$\frac{395}{128}$$ = $$\frac{32 \times 128 - 395 \times 9}{9 \times 128}$$ = $$\frac{4096 - 3555}{1152}$$ = $$\frac{541}{1152}$$.

Ответ: $$\frac{541}{1152}$$

2)

Сначала преобразуем смешанные числа в неправильные дроби:

1$$\frac{31}{35} = \frac{1 \cdot 35 + 31}{35} = \frac{66}{35}$$

2$$\frac{8}{9} = \frac{2 \cdot 9 + 8}{9} = \frac{26}{9}$$

1$$\frac{19}{45} = \frac{1 \cdot 45 + 19}{45} = \frac{64}{45}$$

Теперь решаем по действиям:

1) $$\frac{26}{9} : \frac{64}{45} = \frac{26}{9} \times \frac{45}{64} = \frac{26 \times 45}{9 \times 64} = \frac{13 \times 5}{1 \times 32} = \frac{65}{32}$$

2) $$2 - \frac{65}{32} = \frac{2 \times 32 - 65}{32} = \frac{64 - 65}{32} = -\frac{1}{32}$$

3) $$\frac{66}{35} : (-\frac{1}{32}) = \frac{66}{35} \times (-32) = -\frac{66 \times 32}{35} = -\frac{2112}{35} = -60\frac{12}{35}$$

Ответ: $$-60\frac{12}{35}$$

3)

1) 1$$\frac{1}{35} = \frac{36}{35}$$

2) 1$$\frac{8}{35} = \frac{43}{35}$$

3) $$\frac{36}{35} : \frac{4}{5} = \frac{36}{35} \times \frac{5}{4} = \frac{36 \times 5}{35 \times 4} = \frac{9 \times 1}{7 \times 1} = \frac{9}{7}$$

4) $$\frac{9}{7} - \frac{43}{35} = \frac{9 \times 5 - 43}{35} = \frac{45 - 43}{35} = \frac{2}{35}$$

5) 3$$\frac{1}{3} = \frac{10}{3}$$

6) $$\frac{2}{35} \times \frac{10}{3} = \frac{2 \times 10}{35 \times 3} = \frac{2 \times 2}{7 \times 3} = \frac{4}{21}$$

Ответ: $$\frac{4}{21}$$

4)

1) 1$$\frac{5}{9} = \frac{14}{9}$$

2) 3$$\frac{20}{27} = \frac{101}{27}$$

3) $$\frac{14}{9} : \frac{7}{24} = \frac{14}{9} \times \frac{24}{7} = \frac{2 \times 8}{3 \times 1} = \frac{16}{3}$$

4) 7 - $$\frac{16}{3} = \frac{7 \times 3 - 16}{3} = \frac{21 - 16}{3} = \frac{5}{3}$$

5) $$\frac{5}{3} \times \frac{101}{27} = \frac{5 \times 101}{3 \times 27} = \frac{505}{81} = 6\frac{19}{81}$$

Ответ: 6$$\frac{19}{81}$$

453. Решите уравнение:

1)

$$\frac{25}{27}x = \frac{5}{18}$$

x = $$\frac{5}{18} : \frac{25}{27}$$

x = $$\frac{5}{18} \times \frac{27}{25}$$

x = $$\frac{5 \times 27}{18 \times 25}$$

x = $$\frac{1 \times 3}{2 \times 5}$$

x = $$\frac{3}{10}$$

Ответ: $$\frac{3}{10}$$

2)

$$\frac{13}{17}x = 39$$

x = 39 : $$\frac{13}{17}$$

x = 39 $$\times$$ $$\frac{17}{13}$$

x = $$\frac{39 \times 17}{13}$$

x = $$\frac{3 \times 17}{1}$$

x = 51

Ответ: 51

3)

4x = $$\frac{5}{7}$$

x = $$\frac{5}{7} : 4$$

x = $$\frac{5}{7} \times \frac{1}{4}$$

x = $$\frac{5}{28}$$

Ответ: $$\frac{5}{28}$$

4)

x : 2$$\frac{2}{15} = 1\frac{9}{16}$$

x : $$\frac{32}{15} = \frac{25}{16}$$

x = $$\frac{25}{16} \times \frac{32}{15}$$

x = $$\frac{25 \times 32}{16 \times 15}$$

x = $$\frac{5 \times 2}{1 \times 3}$$

x = $$\frac{10}{3}$$

x = 3$$\frac{1}{3}$$

Ответ: 3$$\frac{1}{3}$$

5)

4$$\frac{4}{9} : x = \frac{5}{27}$$

$$\frac{40}{9} : x = \frac{5}{27}$$

x = $$\frac{40}{9} : \frac{5}{27}$$

x = $$\frac{40}{9} \times \frac{27}{5}$$

x = $$\frac{40 \times 27}{9 \times 5}$$

x = $$\frac{8 \times 3}{1 \times 1}$$

x = 24

Ответ: 24

6)

1$$\frac{4}{9}x = 5,2

$$\frac{13}{9}x = 5.2

x = 5.2 : $$\frac{13}{9}$$

x = 5.2 $$\times$$ $$\frac{9}{13}$$

x = $$\frac{5.2 \times 9}{13}$$

x = $$\frac{46.8}{13}$$

x = 3.6

Ответ: 3.6

464. Решите уравнение:

1)

2$$\frac{2}{11}x - \frac{5}{16} = 1\frac{3}{4}$$

$$\frac{24}{11}x - \frac{5}{16} = \frac{7}{4}$$

$$\frac{24}{11}x = \frac{7}{4} + \frac{5}{16}$$

$$\frac{24}{11}x = \frac{7 \times 4 + 5}{16}$$

$$\frac{24}{11}x = \frac{28 + 5}{16}$$

$$\frac{24}{11}x = \frac{33}{16}$$

x = $$\frac{33}{16} : \frac{24}{11}$$

x = $$\frac{33}{16} \times \frac{11}{24}$$

x = $$\frac{33 \times 11}{16 \times 24}$$

x = $$\frac{3 \times 11 \times 11}{16 \times 8 \times 3}$$

x = $$\frac{363}{384}$$

x = $$\frac{121}{128}$$

Ответ: $$\frac{121}{128}$$

2)

4$$\frac{2}{9}x + 3\frac{5}{14} = 6\frac{11}{21}$$

$$\frac{38}{9}x + \frac{47}{14} = \frac{137}{21}$$

$$\frac{38}{9}x = \frac{137}{21} - \frac{47}{14}$$

$$\frac{38}{9}x = \frac{137 \times 2 - 47 \times 3}{42}$$

$$\frac{38}{9}x = \frac{274 - 141}{42}$$

$$\frac{38}{9}x = \frac{133}{42}$$

x = $$\frac{133}{42} : \frac{38}{9}$$

x = $$\frac{133}{42} \times \frac{9}{38}$$

x = $$\frac{133 \times 9}{42 \times 38}$$

x = $$\frac{133 \times 3}{14 \times 38}$$

x = $$\frac{7 \times 19 \times 3}{2 \times 7 \times 2 \times 19}$$

x = $$\frac{3}{4}$$

Ответ: $$\frac{3}{4}$$

3)

$$\frac{11}{18} - \frac{14}{27}x = \frac{5}{12}$$

-$$\frac{14}{27}x = \frac{5}{12} - \frac{11}{18}$$

-$$\frac{14}{27}x = \frac{5 \times 3 - 11 \times 2}{36}$$

-$$\frac{14}{27}x = \frac{15 - 22}{36}$$

-$$\frac{14}{27}x = -\frac{7}{36}$$

x = -$$\frac{7}{36} : -\frac{14}{27}$$

x = $$\frac{7}{36} \times \frac{27}{14}$$

x = $$\frac{7 \times 27}{36 \times 14}$$

x = $$\frac{1 \times 3}{4 \times 2}$$

x = $$\frac{3}{8}$$

Ответ: $$\frac{3}{8}$$

4)

$$\frac{1}{3}x + \frac{1}{4}x + \frac{1}{5}x = 1\frac{19}{75}$$

$$\frac{1}{3}x + \frac{1}{4}x + \frac{1}{5}x = \frac{94}{75}$$

$$\frac{20x + 15x + 12x}{60} = \frac{94}{75}$$

$$\frac{47x}{60} = \frac{94}{75}$$

x = $$\frac{94}{75} : \frac{47}{60}$$

x = $$\frac{94}{75} \times \frac{60}{47}$$

x = $$\frac{94 \times 60}{75 \times 47}$$

x = $$\frac{2 \times 4 \times 3}{5 \times 1}$$

x = $$\frac{8}{5}$$

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

Ответ: 1$$\frac{3}{5}$$

5)

4$$\frac{1}{2} : x + 1\frac{3}{4} = 3\frac{19}{28}$$

$$\frac{9}{2} : x + \frac{7}{4} = \frac{103}{28}$$

$$\frac{9}{2} : x = \frac{103}{28} - \frac{7}{4}$$

$$\frac{9}{2} : x = \frac{103 - 7 \times 7}{28}$$

$$\frac{9}{2} : x = \frac{103 - 49}{28}$$

$$\frac{9}{2} : x = \frac{54}{28}$$

$$\frac{9}{2} : x = \frac{27}{14}$$

x = $$\frac{9}{2} : \frac{27}{14}$$

x = $$\frac{9}{2} \times \frac{14}{27}$$

x = $$\frac{9 \times 14}{2 \times 27}$$

x = $$\frac{1 \times 7}{1 \times 3}$$

x = $$\frac{7}{3}$$

x = 2$$\frac{1}{3}$$

Ответ: 2$$\frac{1}{3}$$

6)

3$$\frac{2}{3}:(x - 2\frac{4}{15}) = 3\frac{5}{13}$$

$$\frac{11}{3} : (x - \frac{34}{15}) = \frac{44}{13}$$

x - $$\frac{34}{15} = \frac{11}{3} : \frac{44}{13}$$

x - $$\frac{34}{15} = \frac{11}{3} \times \frac{13}{44}$$

x - $$\frac{34}{15} = \frac{11 \times 13}{3 \times 44}$$

x - $$\frac{34}{15} = \frac{1 \times 13}{3 \times 4}$$

x - $$\frac{34}{15} = \frac{13}{12}$$

x = $$\frac{13}{12} + \frac{34}{15}$$

x = $$\frac{13 \times 5 + 34 \times 4}{60}$$

x = $$\frac{65 + 136}{60}$$

x = $$\frac{201}{60}$$

x = $$\frac{67}{20}$$

x = 3$$\frac{7}{20}$$

Ответ: 3$$\frac{7}{20}$$

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