Упр.1 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) $$2\frac{1}{3}\cdot 9-1\frac{1}{3}\cdot 3\frac{1}{4}-2\frac{2}{7}\cdot 3\frac{5}{24}$$

$$=\frac{7}{3}\cdot 9-\frac{4}{3}\cdot \frac{13}{4}-\frac{16}{7}\cdot \frac{77}{24}$$

$$=21-\frac{13}{3}-\frac{22}{3}=21-\frac{35}{3}=16\frac{2}{3}$$

2) $$1\frac{7}{48}\cdot 2\frac{2}{5}-\left(9\frac{1}{6}\cdot \frac{4}{15}+2\frac{5}{9}\right)\cdot \frac{2}{5}$$

$$=\frac{55}{48}\cdot \frac{12}{5}-\left(\frac{55}{6}\cdot \frac{4}{15}+\frac{23}{9}\right)\cdot \frac{2}{5}$$

$$=\frac{11}{4}-\left(\frac{22}{9}+\frac{23}{9}\right)\cdot \frac{2}{5}=\frac{11}{4}-5\cdot \frac{2}{5}=\frac{11}{4}-2=\frac{3}{4}$$

3) $$\left(2\frac{1}{4}+4\frac{5}{6}\right):3\frac{2}{5}-\frac{3}{4}:\frac{3}{5}$$

$$=\left(\frac{9}{4}+\frac{29}{6}\right):\frac{17}{5}-\frac{3}{4}\cdot \frac{5}{3}$$

$$=\frac{85}{12}\cdot \frac{5}{17}-\frac{5}{4}=\frac{25}{12}-\frac{15}{12}=\frac{5}{6}$$

4) $$\left(3{,}04:\frac{1}{30}-16{,}03:\frac{7}{20}\right)\cdot \frac{1}{5}+0{,}072\cdot \frac{1}{3}$$

$$=\left(\frac{304}{100}\cdot 30-\frac{1603}{100}\cdot \frac{20}{7}\right)\cdot \frac{1}{5}+\frac{72}{1000}\cdot \frac{1}{3}$$

$$=\left(\frac{456}{5}-\frac{229}{5}\right)\cdot \frac{1}{5}+\frac{3}{125}=\frac{227}{5}\cdot \frac{1}{5}+\frac{3}{125}$$

$$=\frac{227}{25}+\frac{3}{125}=\frac{1135}{125}+\frac{3}{125}=\frac{1138}{125}=9{,}104$$

5) $$\left(-28{,}6:57{,}2-2{,}68:(-1{,}34)\right)\cdot (-3{,}2)$$

$$=\left(-0{,}5-(-2)\right)\cdot (-3{,}2)=1{,}5\cdot (-3{,}2)=-4{,}8$$

6) $$\left(-1{,}7+3{,}64:(-1{,}4)\right):(-0{,}001)\cdot (-0{,}4)$$

$$=\left(-1{,}7-2{,}6\right):(-0{,}001)\cdot (-0{,}4)=-4{,}3:(-0{,}001)\cdot (-0{,}4)$$

$$=4300\cdot (-0{,}4)=-1720$$

7) $$\left(\frac{9}{14}-\left(-\frac{5}{21}\right)\right):\left(-2\frac{9}{14}\right)$$

$$=\left(\frac{27}{42}+\frac{10}{42}\right):\left(-\frac{37}{14}\right)=\frac{37}{42}\cdot \left(-\frac{14}{37}\right)=-\frac{1}{3}$$

8) $$\left(\frac{7}{16}-\frac{31}{40}\right):\left(-\frac{17}{24}+\frac{27}{40}\right)$$

$$=\left(\frac{35}{80}-\frac{62}{80}\right):\left(-\frac{85}{120}+\frac{81}{120}\right)=\left(-\frac{27}{80}\right):\left(-\frac{1}{30}\right)$$

$$=\frac{27}{80}\cdot 30=\frac{81}{8}=10\frac{1}{8}$$

9) $$-3\frac{3}{4}-\left(-8\frac{2}{9}-(-4{,}5):\frac{9}{14}\right)\cdot 2\frac{1}{4}$$

$$=-3\frac{3}{4}-\left(-8\frac{2}{9}+\frac{45}{10}\cdot \frac{14}{9}\right)\cdot \frac{9}{4}$$

$$=-3\frac{3}{4}-\left(-8\frac{2}{9}+7\right)\cdot \frac{9}{4}=-3\frac{3}{4}-\left(-1\frac{2}{9}\right)\cdot \frac{9}{4}$$

$$=-3\frac{3}{4}+\frac{11}{9}\cdot \frac{9}{4}=-3\frac{3}{4}+2\frac{3}{4}=-1$$

Ответ: 1) $$16\frac{2}{3}$$; 2) $$\frac{3}{4}$$; 3) $$\frac{5}{6}$$; 4) $$9{,}104$$; 5) $$-4{,}8$$; 6) $$-1720$$; 7) $$-\frac{1}{3}$$; 8) $$10\frac{1}{8}$$; 9) $$-1$$.