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

1) 9 1/4 · 8 — 3 2/3 · 4 1/2 — 10 4/5 · 4 7/12;
2) 1 1/22 · 3 2/3 — (2 5/6 + 3 5/6 · 7/23) · 3/5;
3) (3 1/4 + 2 1/6) : 2 3/5 — 2/3 : 4/9;
4) (5,07 : 1/20 — 23,4 : 13/50) · 1/4 + 0,074 · 1/2;
5) (-31,7 : 63,4 — 23,4 : (-11,7)) · (-2,4);
6) (-1,2 + 4,32 : (-1,8)) : (-0,001) · (-0,3);
7) (7/16 — (-5/24)) : (-1 15/16);
8) (10/21 — 25/28) : (-11/14 + 24/35);
9) -2 2/3 + 2 1/3 · (-15 3/7 — (-4,8) : 4/15).

1. $$9\frac14\cdot 8-3\frac23\cdot 4\frac12-10\frac45\cdot 4\frac7{12}$$
   $$=\frac{37}{4}\cdot 8-\frac{11}{3}\cdot \frac92-\frac{54}{5}\cdot \frac{55}{12}$$
   $$=74-\frac{11\cdot 3}{1\cdot 2}-\frac{9\cdot 11}{1\cdot 2}=74-\frac{33}{2}-\frac{99}{2}=74-66=8.$$

2. $$1\frac1{22}\cdot 3\frac23-\left(2\frac56+3\frac56\cdot \frac7{23}\right)\cdot \frac35$$
   $$=\frac{23}{22}\cdot \frac{11}{3}-\left(\frac{17}{6}+\frac{23}{6}\cdot \frac7{23}\right)\cdot \frac35$$
   $$=\frac{23}{6}-\left(\frac{17}{6}+\frac76\right)\cdot \frac35=\frac{23}{6}-4\cdot \frac35$$
   $$=\frac{23}{6}-\frac{12}{5}=\frac{115-72}{30}=\frac{43}{30}=1\frac{13}{30}.$$

3. $$\left(3\frac14+2\frac16\right):2\frac35-\frac23:\frac49$$
   $$=\left(\frac{13}{4}+\frac{13}{6}\right):\frac{13}{5}-\frac23\cdot \frac94$$
   $$=\frac{65}{12}\cdot \frac{5}{13}-\frac{18}{12}=\frac{25}{12}-\frac{18}{12}=\frac{7}{12}.$$

4. $$\left(5{,}07:\frac1{20}-23{,}4:\frac{13}{50}\right)\cdot \frac14+0{,}074\cdot \frac12$$
   $$=\left(\frac{507}{100}\cdot 20-\frac{234}{10}\cdot \frac{50}{13}\right)\cdot \frac14+\frac{74}{1000}\cdot \frac12$$
   $$=\left(\frac{507}{5}-90\right)\cdot \frac14+0{,}037$$
   $$=11\frac25\cdot \frac14+0{,}037=\frac{57}{20}+0{,}037=2{,}85+0{,}037=2{,}887.$$

5. $$(-31{,}7:63{,}4-23{,}4:(-11{,}7))\cdot (-2{,}4)$$
   $$=(-0{,}5+2)\cdot (-2{,}4)=1{,}5\cdot (-2{,}4)=-3{,}6.$$

6. $$(-1{,}2+4{,}32:(-1{,}8)):(-0{,}001)\cdot (-0{,}3)$$
   $$=(-1{,}2-2{,}4):(-0{,}001)\cdot (-0{,}3)$$
   $$=-3{,}6:(-0{,}001)\cdot (-0{,}3)=3600\cdot (-0{,}3)=-1080.$$

7. $$\left(\frac7{16}-\left(-\frac5{24}\right)\right):\left(-1\frac{15}{16}\right)$$
   $$=\left(\frac7{16}+\frac5{24}\right):\left(-\frac{31}{16}\right)$$
   $$=\left(\frac{21}{48}+\frac{10}{48}\right):\left(-\frac{31}{16}\right)=\frac{31}{48}\cdot \left(-\frac{16}{31}\right)=-\frac13.$$

8. $$\left(\frac{10}{21}-\frac{25}{28}\right):\left(-\frac{11}{14}+\frac{24}{35}\right)$$
   $$=\left(\frac{40}{84}-\frac{75}{84}\right):\left(-\frac{55}{70}+\frac{48}{70}\right)$$
   $$=-\frac{35}{84}:\left(-\frac7{70}\right)=\frac{5}{12}:\frac{1}{10}=\frac{5}{12}\cdot 10=\frac{25}{6}=4\frac16.$$

9. $$-2\frac23+2\frac13\cdot \left(-15\frac37-(-4{,}8):\frac4{15}\right)$$
   $$=-2\frac23+\frac73\cdot \left(-15\frac37+4{,}8\cdot \frac{15}{4}\right)$$
   $$=-2\frac23+\frac73\cdot \left(-15\frac37+18\right)$$
   $$=-2\frac23+\frac73\cdot 2\frac47=-2\frac23+\frac73\cdot \frac{18}{7}=-2\frac23+6=3\frac13.$$

Ответ

1) $$8$$; 2) $$1\frac{13}{30}$$; 3) $$\frac{7}{12}$$; 4) $$2{,}887$$; 5) $$-3{,}6$$; 6) $$-1080$$; 7) $$-\frac13$$; 8) $$4\frac16$$; 9) $$3\frac13$$.