Упр.824 ГДЗ Никольский Потапов 9 класс (Алгебра)

б) ((1 13/16+1 17/24)·4/13)/((28 14/15):2,8-4 11/12);
в) (4,58+6,275:(1,25^3-1,25^2·0,45)/(49,533:16,5+2,522);
г) (1,476+2,08·4,05)/(49,938:(0,16·12,34^2-0,16^3)-0,25;
д) (42,5904:6,08-1,245)/((18,2^2-5,6^2+23,8·7,4):5,95+35,2).

1. а)

   $$\frac{8{,}4\cdot\left(1\frac{5}{8}+\frac{17}{18}\right)-15\frac{59}{60}}{646{,}8:21}$$
   $$= \frac{\frac{84}{10}\cdot\left(\frac{13}{8}+\frac{17}{18}\right)-\frac{959}{60}}{\frac{6468}{10}:21}$$
   $$= \frac{\frac{42}{5}\cdot\frac{185}{72}-\frac{959}{60}}{30{,}8} = \frac{\frac{7\cdot185}{12\cdot5}-\frac{959}{60}}{30{,}8}$$
   $$= \frac{\frac{1295-959}{60}}{30{,}8} = \frac{\frac{336}{60}}{30{,}8} = \frac{336}{60\cdot308} = \frac{12}{11}.$$

2. б)

   $$\frac{\left(1\frac{13}{16}+1\frac{17}{24}\right)\cdot\frac{4}{13}}{\left(28\frac{14}{15}\right):2{,}8-4\frac{11}{12}}$$
   $$= \frac{\left(\frac{29}{16}+\frac{41}{24}\right)\cdot\frac{4}{13}}{\frac{434}{15}: \frac{28}{10}-\frac{59}{12}} = \frac{\frac{87+82}{48}\cdot\frac{4}{13}}{\frac{434}{15}\cdot\frac{5}{14}-\frac{59}{12}}$$
   $$= \frac{\frac{169}{48}\cdot\frac{4}{13}}{\frac{31}{3}-\frac{59}{12}} = \frac{\frac{13}{12}}{\frac{124-59}{12}} = \frac{13}{12}:\frac{65}{12} = \frac{13}{65} = \frac{1}{5} = 0{,}2.$$

3. в)

   $$\frac{4{,}58+6{,}275:(1{,}25^3-1{,}25^2\cdot0{,}45)}{49{,}533:16{,}5+2{,}522}$$
   $$= \frac{4{,}58+6{,}275:\bigl(1{,}25^2\cdot(1{,}25-0{,}45)\bigr)}{3{,}002+2{,}522} = \frac{4{,}58+6{,}275:(1{,}25^2\cdot0{,}8)}{5{,}524}$$
   $$= \frac{4{,}58+6{,}275:1{,}25}{5{,}524} = \frac{4{,}58+5{,}02}{5{,}524} = \frac{9{,}6}{5{,}524} = \frac{9600}{5524} = \frac{2400}{1381} = 1\frac{1019}{1381}.$$

4. г)

   $$\frac{1{,}476+2{,}08\cdot4{,}05}{49{,}938:(0{,}16\cdot12{,}34^2-0{,}16^3)-0{,}25}$$
   $$= \frac{1{,}476+8{,}424}{49{,}938:\bigl(0{,}16\cdot(12{,}34-0{,}16)(12{,}34+0{,}16)\bigr)-0{,}25}$$
   $$= \frac{9{,}9}{312{,}1125:(12{,}18\cdot12{,}5)-0{,}25} = \frac{9{,}9}{2{,}05-0{,}25} = \frac{9{,}9}{1{,}8} = \frac{99}{18} = 5{,}5.$$

5. д)

   $$\frac{42{,}5904:6{,}08-1{,}245}{(18{,}2^2-5{,}6^2+23{,}8\cdot7{,}4):5{,}95+35{,}2}$$
   $$= \frac{7{,}005-1{,}245}{\bigl((18{,}2-5{,}6)(18{,}2+5{,}6)+176{,}12\bigr):5{,}95+35{,}2}$$
   $$= \frac{5{,}76}{(12{,}6\cdot23{,}8+176{,}12):5{,}95+35{,}2} = \frac{5{,}76}{(299{,}88+176{,}12):5{,}95+35{,}2}$$
   $$= \frac{5{,}76}{476:5{,}95+35{,}2} = \frac{5{,}76}{80+35{,}2} = \frac{5{,}76}{115{,}2} = \frac{576}{11520} = 0{,}05.$$

Ответ

а) $$\frac{12}{11}$$; б) $$0{,}2$$; в) $$1\frac{1019}{1381}$$; г) $$5{,}5$$; д) $$0{,}05$$.