Упр.1032 Часть 2 ГДЗ Дорофеев Петерсон 5 класс (Математика)

а) (((12 — (2 1/2 · 3 + 9 : 5))/((1 7/8 + 2 11/12) : 3 5/6 + 0,1))^3;
б) (((1 1/2 + 2 1/3 + 3 1/4) : 4 1/4)/(4 — 10 1/2 : 4 1/2))^2 + ((8 1/4 : 1 3/8 + 5 1/2 · 1 3/4)/((5/6 + (4 5/6 + 7 2/3) : 2 6/7)))^2.

а)

$$ \left(\frac{12-\left(2\frac{1}{2}\cdot 3+9:5\right)}{\left(1\frac{7}{8}+2\frac{11}{12}\right):3\frac{5}{6}+0{,}1}\right)^3 $$

Найдём числитель:

$$ 2\frac{1}{2}\cdot 3+9:5=\frac{5}{2}\cdot 3+\frac{9}{5}=\frac{15}{2}+\frac{9}{5}=7\frac{1}{2}+1\frac{4}{5}=9\frac{3}{10} $$
$$ 12-9\frac{3}{10}=2\frac{7}{10} $$

Найдём знаменатель:

$$ \left(1\frac{7}{8}+2\frac{11}{12}\right):3\frac{5}{6}+0{,}1 = \left(\frac{15}{8}+\frac{35}{12}\right):\frac{23}{6}+0{,}1 $$
$$ \frac{15}{8}+\frac{35}{12}=\frac{115}{24} $$
$$ \frac{115}{24}:\frac{23}{6}=\frac{115}{24}\cdot\frac{6}{23}=\frac{5}{4} $$
$$ \frac{5}{4}+0{,}1=\frac{5}{4}+\frac{1}{10}=1\frac{7}{20} $$

Тогда

$$ \frac{2\frac{7}{10}}{1\frac{7}{20}}=\frac{27}{10}:\frac{27}{20}=2 $$
$$ 2^3=8 $$

б)

$$ \left(\frac{\left(1\frac{1}{2}+2\frac{1}{3}+3\frac{1}{4}\right):4\frac{1}{4}}{4-10\frac{1}{2}:4\frac{1}{2}}\right)^2 + \left(\frac{8\frac{1}{4}:1\frac{3}{8}+5\frac{1}{2}\cdot 1\frac{3}{4}}{\frac{5}{6}+\left(4\frac{5}{6}+7\frac{2}{3}\right):2\frac{6}{7}}\right)^2 $$

Первую дробь вычислим:

$$ 1\frac{1}{2}+2\frac{1}{3}+3\frac{1}{4} = \frac{3}{2}+\frac{7}{3}+\frac{13}{4} = \frac{85}{12} $$
$$ \frac{85}{12}:4\frac{1}{4} = \frac{85}{12}:\frac{17}{4} = \frac{85}{12}\cdot\frac{4}{17} = \frac{5}{3} $$
$$ 10\frac{1}{2}:4\frac{1}{2} = \frac{21}{2}:\frac{9}{2} = \frac{21}{9} = \frac{7}{3} $$
$$ 4-\frac{7}{3}=1\frac{2}{3} $$
$$ \frac{5}{3}:1\frac{2}{3} = \frac{5}{3}:\frac{5}{3} =1 $$
$$ 1^2=1 $$

Вторую дробь вычислим:

$$ 8\frac{1}{4}:1\frac{3}{8} = \frac{33}{4}:\frac{11}{8} = \frac{33}{4}\cdot\frac{8}{11} =6 $$
$$ 5\frac{1}{2}\cdot 1\frac{3}{4} = \frac{11}{2}\cdot\frac{7}{4} = \frac{77}{8} = 9\frac{5}{8} $$
$$ 6+9\frac{5}{8}=15\frac{5}{8} $$

Знаменатель второй дроби:

$$ 4\frac{5}{6}+7\frac{2}{3} = \frac{29}{6}+\frac{23}{3} = \frac{75}{6} = 12\frac{1}{2} $$
$$ 12\frac{1}{2}:2\frac{6}{7} = \frac{25}{2}:\frac{20}{7} = \frac{25}{2}\cdot\frac{7}{20} = \frac{35}{8} $$
$$ \frac{5}{6}+\frac{35}{8} = \frac{20}{24}+\frac{105}{24} = \frac{125}{24} = 5\frac{5}{24} $$

Тогда

$$ 15\frac{5}{8}:5\frac{5}{24} = \frac{125}{8}:\frac{125}{24} = 3 $$
$$ 3^2=9 $$

$$ 1+9=10 $$

Ответ

а) 8; б) 10.