Упр.1 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) 4 1/7 · 14 — 2 1/4 · 3 1/6 — 1 1/9 · 3 3/8;
2) 1 31/32 · 3 1/5 — (8 5/9 · 6/35 + 2 2/15) · 5/12;
3) (4 5/12 — 3 13/24) : 1 3/4 + 5/6 : 5/7;
4) (2,06 : 1/60 — 14,84 : 7/60) · 1/6 — 0,084 · 1/12;
5) (-16,2 : 32,4 — 21,2 :(-10,6)) · (-2,8);
6) (-2,3 — 3,91 : (-2,3)) : (-0,01) · (-0,7);
7) (-11/15 — 7/20) : (-3 1/4);
8) (-11/18 + 29/45) : (19/27 — 35/54);
9) -4 1/7 + 2 1/4 · (-11 2/9 — (-5,4) : 9/35).

1. $$4\frac{1}{7}\cdot 14-2\frac{1}{4}\cdot 3\frac{1}{6}-1\frac{1}{9}\cdot 3\frac{3}{8}$$
   $$=\frac{29}{7}\cdot 14-\frac{9}{4}\cdot \frac{19}{6}-\frac{10}{9}\cdot \frac{27}{8}$$
   $$=58-\frac{57}{8}-\frac{15}{4}=58-7\frac{1}{8}-3\frac{3}{4}=47\frac{1}{8}.$$

2. $$1\frac{31}{32}\cdot 3\frac{1}{5}-\left(8\frac{5}{9}\cdot \frac{6}{35}+2\frac{2}{15}\right)\cdot \frac{5}{12}$$
   $$=\frac{63}{32}\cdot \frac{16}{5}-\left(\frac{77}{9}\cdot \frac{6}{35}+\frac{2}{15}\right)\cdot \frac{5}{12}$$
   $$=\frac{63}{10}-\left(\frac{22}{15}+\frac{2}{15}\right)\cdot \frac{5}{12}$$
   $$=\frac{63}{10}-2\cdot \frac{5}{12}=\frac{63}{10}-\frac{5}{6}=6\frac{3}{10}-\frac{5}{6}=4{,}8.$$

3. $$(4\frac{5}{12}-3\frac{13}{24}):1\frac{3}{4}+\frac{5}{6}:\frac{5}{7}$$
   $$=\left(4\frac{10}{24}-3\frac{13}{24}\right):\frac{7}{4}+\frac{5}{6}:\frac{5}{7}$$
   $$=\frac{21}{24}:\frac{7}{4}+\frac{5}{6}\cdot \frac{7}{5}=\frac{7}{8}\cdot \frac{4}{7}+\frac{7}{6}$$
   $$=\frac{1}{2}+\frac{7}{6}=1\frac{2}{3}.$$

4. $$(2{,}06:\frac{1}{60}-14{,}84:\frac{7}{60})\cdot \frac{1}{6}-0{,}084\cdot \frac{1}{12}$$
   $$=(2{,}06\cdot 60-14{,}84\cdot \frac{60}{7})\cdot \frac{1}{6}-0{,}007$$
   $$=(2{,}06\cdot 60-2{,}12\cdot 60)\cdot \frac{1}{6}-0{,}007$$
   $$=60\cdot (2{,}06-2{,}12)\cdot \frac{1}{6}-0{,}007$$
   $$=60\cdot (-0{,}06)\cdot \frac{1}{6}-0{,}007=-0{,}6-0{,}007=-0{,}607.$$

5. $$(-16{,}2:32{,}4-21{,}2:(-10{,}6))\cdot (-2{,}8)$$
   $$=\left(-\frac{1}{2}+2\right)\cdot (-2{,}8)=\frac{3}{2}\cdot \left(-\frac{14}{5}\right)=-\frac{42}{10}=-4{,}2.$$

6. $$(-2{,}3-3{,}91:(-2{,}3)):(-0{,}01)\cdot (-0{,}7)$$
   $$=(-2{,}3+1{,}7):(-0{,}01)\cdot (-0{,}7)$$
   $$=-0{,}6:(-0{,}01)\cdot (-0{,}7)=60\cdot (-0{,}7)=-42.$$

7. $$\left(-\frac{11}{15}-\frac{7}{20}\right):\left(-3\frac{1}{4}\right)$$
   $$=\left(-\frac{44}{60}-\frac{21}{60}\right):\left(-\frac{13}{4}\right)$$
   $$=-\frac{65}{60}\cdot \left(-\frac{4}{13}\right)=\frac{1}{3}.$$

8. $$\left(-\frac{11}{18}+\frac{29}{45}\right):\left(\frac{19}{27}-\frac{35}{54}\right)$$
   $$=\left(-\frac{55}{90}+\frac{58}{90}\right):\left(\frac{38}{54}-\frac{35}{54}\right)$$
   $$=\frac{3}{90}:\frac{3}{54}=\frac{1}{30}:\frac{1}{18}=\frac{18}{30}=\frac{3}{5}=0{,}6.$$

9. $$-4\frac{1}{7}+2\frac{1}{4}\cdot \left(-11\frac{2}{9}-(-5{,}4):\frac{9}{35}\right)$$
   $$=-4\frac{1}{7}+\frac{9}{4}\cdot \left(-11\frac{2}{9}+\frac{54}{10}:\frac{9}{35}\right)$$
   $$=-4\frac{1}{7}+\frac{9}{4}\cdot \left(-11\frac{2}{9}+21\right)$$
   $$=-4\frac{1}{7}+\frac{9}{4}\cdot 9\frac{7}{9}$$
   $$=-4\frac{1}{7}+22=17\frac{6}{7}.$$

Ответ

1) $$47\frac{1}{8}$$; 2) $$4{,}8$$; 3) $$1\frac{2}{3}$$; 4) $$-0{,}607$$; 5) $$-4{,}2$$; 6) $$-42$$; 7) $$\frac{1}{3}$$; 8) $$\frac{3}{5}$$; 9) $$17\frac{6}{7}$$.