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

1) 2 1/3 · 9 — 1 1/3 · 3 1/4 — 2 2/7 · 3 5/24;
2) 1 7/48 · 2 2/5 — (9 1/6 · 4/15 + 2 5/9) · 2/5;
3) (2 1/4 + 4 5/6) : 3 2/5 — 3/4 : 3/5;
4) (3,04 : 1/30 — 16,03 : 7/20) · 1/5 + 0,072 · 1/3;
5) (-28,6 : 57,2 — 2,68 : (-1,34)) · (-3,2);
6) (-1,7 + 3,64 : (-1,4)) : (-0,001) · (-0,4);
7) (9/14 — (-5/21)) : (-2 9/14);
8) (7/16 — 31/40) : (-17/24 + 27/40);
9) -3 3/4 — (-8 2/9 — (-4,5) : 9/14) · 2 1/4.

1. $$2\frac{1}{3}\cdot 9-1\frac{1}{3}\cdot 3\frac{1}{4}-2\frac{2}{7}\cdot 3\frac{5}{24}$$
   $$=\frac{7}{3}\cdot 9-\frac{4}{3}\cdot \frac{13}{4}-\frac{16}{7}\cdot \frac{77}{24}$$
   $$=21-\frac{13}{3}-\frac{22}{3}=21-\frac{35}{3}=9\frac{1}{3}.$$

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. $$(2\frac{1}{4}+4\frac{5}{6}) : 3\frac{2}{5}-\frac{3}{4}:\frac{3}{5}$$
   $$=\left(\frac{9}{4}+\frac{29}{6}\right):\frac{17}{5}-\frac{3}{4}\cdot \frac{5}{3}$$
   $$=\frac{85}{12}:\frac{17}{5}-\frac{5}{4}$$
   $$=\frac{85}{12}\cdot \frac{5}{17}-\frac{5}{4}=\frac{25}{12}-\frac{15}{12}=\frac{5}{6}.$$

4. $$(3{,}04:\frac{1}{30}-16{,}03:\frac{7}{20})\cdot \frac{1}{5}+0{,}072\cdot \frac{1}{3}$$
   $$=\left(3{,}04\cdot 30-16{,}03\cdot \frac{20}{7}\right)\cdot \frac{1}{5}+0{,}024$$
   $$=\left(91{,}2-45{,}\overline{4}\right)\cdot \frac{1}{5}+0{,}024$$
   $$=45{,}76\cdot \frac{1}{5}+0{,}024=9{,}152+0{,}024=9{,}176.$$

5. $$(-28{,}6:57{,}2-2{,}68:(-1{,}34))\cdot (-3{,}2)$$
   $$=(-0{,}5-(-2))\cdot (-3{,}2)$$
   $$=1{,}5\cdot (-3{,}2)=-4{,}8.$$

6. $$(-1{,}7+3{,}64:(-1{,}4)):(-0{,}001)\cdot (-0{,}4)$$
   $$=(-1{,}7-2{,}6):(-0{,}001)\cdot (-0{,}4)$$
   $$=-4{,}3:(-0{,}001)\cdot (-0{,}4)$$
   $$=4300\cdot (-0{,}4)=-1720.$$

7. $$(\frac{9}{14}-(-\frac{5}{21})):(-2\frac{9}{14})$$
   $$=\left(\frac{27}{42}+\frac{10}{42}\right):\left(-\frac{37}{14}\right)$$
   $$=\frac{37}{42}\cdot \left(-\frac{14}{37}\right)=-\frac{1}{3}.$$

8. $$(\frac{7}{16}-\frac{31}{40}):\left(-\frac{17}{24}+\frac{27}{40}\right)$$
   $$=\left(\frac{35}{80}-\frac{62}{80}\right):\left(-\frac{85}{120}+\frac{81}{120}\right)$$
   $$=-\frac{27}{80}:\left(-\frac{1}{30}\right)=\frac{27}{80}\cdot 30=\frac{81}{8}=10\frac{1}{8}.$$

9. $$-3\frac{3}{4}-\left(-8\frac{2}{9}-(-4{,}5):\frac{9}{14}\right)\cdot 2\frac{1}{4}$$
   $$=-3\frac{3}{4}-\left(-8\frac{2}{9}+\frac{9}{2}:\frac{9}{14}\right)\cdot \frac{9}{4}$$
   $$=-3\frac{3}{4}-\left(-8\frac{2}{9}+7\right)\cdot \frac{9}{4}$$
   $$=-3\frac{3}{4}-\left(-1\frac{2}{9}\right)\cdot \frac{9}{4}$$
   $$=-3\frac{3}{4}+\frac{11}{9}\cdot \frac{9}{4}=-3\frac{3}{4}+\frac{11}{4}=-1.$$

Ответ

1) $$9\frac{1}{3}$$; 2) $$\frac{3}{4}$$; 3) $$\frac{5}{6}$$; 4) $$9{,}176$$; 5) $$-4{,}8$$; 6) $$-1720$$; 7) $$-\frac{1}{3}$$; 8) $$10\frac{1}{8}$$; 9) $$-1$$.