Упр.615 ГДЗ Никольский Потапов 8 класс (Алгебра)

б) (2/15 + 1*7/12) * 30/103 — (2:2*1/4)*9/32;
в) (1/2 + 0,8-3/5) * (3+5*8/25 — 0,12);
г) (2*3/4 + 0,15-1*8/25) : (2*1/2 — 1*3/4 + 0,04);
д) (2,314 — 1/4) : 1/50 + (1*11/16 + 0,7125) :3;
е) 1,456 : 7/25 + 5/16:0,125 + 4*1/2*0,8;
ж) 3*3/4 * 1*1/5 + (2,55 + 2,7):(0,1-1/80);
з) 3,075 : 1,5 -1/4*(/25+3,26);
и) (1*11/24 + 13/36)*1,44 — 8/15*0,5625;
к) 2,88 * 35/72 + (1,0625 — 5/12)*16.

1. а)

   $$2\frac{3}{4} : \left(1\frac{1}{2}-\frac{2}{5}\right)+\left(\frac{3}{4}+\frac{5}{6}\right):3\frac{1}{6}$$
   $$=\frac{11}{4}:\left(\frac{3}{2}-\frac{2}{5}\right)+\frac{19}{12}:\frac{19}{6}$$
   $$=\frac{11}{4}:\frac{11}{10}+\frac{19}{12}\cdot\frac{6}{19}$$
   $$=\frac{11}{4}\cdot\frac{10}{11}+\frac{1}{2}=\frac{5}{2}+\frac{1}{2}=3.$$

2. б)

   $$\left(\frac{2}{15}+1\frac{7}{12}\right)\cdot\frac{30}{103}-\left(2:2\frac{1}{4}\right)\cdot\frac{9}{32}$$
   $$=\left(\frac{2}{15}+\frac{19}{12}\right)\cdot\frac{30}{103}-\left(2:\frac{9}{4}\right)\cdot\frac{9}{32}$$
   $$=\frac{103}{60}\cdot\frac{30}{103}-\frac{8}{9}\cdot\frac{9}{32}$$
   $$=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}.$$

3. в)

   $$\left(\frac{1}{2}+0{,}8-\frac{3}{5}\right)\cdot\left(3+5\frac{8}{25}-0{,}12\right)$$
   $$=(0{,}5+0{,}8-0{,}6)\cdot(3+5{,}32-0{,}12)$$
   $$=0{,}7\cdot 8{,}2=5{,}74.$$

4. г)

   $$\left(2\frac{3}{4}+0{,}15-1\frac{8}{25}\right):\left(2\frac{1}{2}-1\frac{3}{4}+0{,}04\right)$$
   $$=(2{,}75+0{,}15-1{,}32):(2{,}5-1{,}75+0{,}04)$$
   $$=1{,}58:0{,}79=2.$$

5. д)

   $$\left(2{,}314-\frac{1}{4}\right):\frac{1}{50}+\left(1\frac{11}{16}+0{,}7125\right):3$$
   $$=(2{,}314-0{,}25):0{,}02+(1{,}6875+0{,}7125):3$$
   $$=2{,}064:0{,}02+2{,}4:3$$
   $$=103{,}2+0{,}8=104.$$

6. е)

   $$1{,}456:\frac{7}{25}+\frac{5}{16}:0{,}125+4\frac{1}{2}\cdot 0{,}8$$
   $$=1{,}456:0{,}28+0{,}3125:0{,}125+4{,}5\cdot 0{,}8$$
   $$=5{,}2+2{,}5+3{,}6=11{,}3.$$

7. ж)

   $$3\frac{3}{4}\cdot 1\frac{1}{5}+\left(2{,}55+2{,}7\right):\left(0{,}1-\frac{1}{80}\right)$$
   $$=\frac{15}{4}\cdot\frac{6}{5}+5{,}25:\left(\frac{1}{10}-\frac{1}{80}\right)$$
   $$=\frac{9}{2}+\frac{21}{4}:\frac{7}{80}$$
   $$=4{,}5+\frac{21}{4}\cdot\frac{80}{7}=4{,}5+60=64{,}5.$$

8. з)

   $$3{,}075:1{,}5-\frac{1}{4}\left(\frac{1}{25}+3{,}26\right)$$
   $$=2{,}05-\frac{1}{4}\cdot 3{,}3$$
   $$=2{,}05-0{,}825=1{,}225.$$

9. и)

   $$\left(1\frac{11}{24}+\frac{13}{36}\right)\cdot 1{,}44-\frac{8}{15}\cdot 0{,}5625$$
   $$=\left(1\frac{33}{72}+\frac{26}{72}\right)\cdot\frac{144}{100}-\frac{8}{15}\cdot\frac{5625}{10000}$$
   $$=1\frac{59}{72}\cdot 1\frac{11}{25}-\frac{3}{10}$$
   $$=\frac{131}{72}\cdot\frac{36}{25}-\frac{3}{10}$$
   $$=\frac{131}{50}-\frac{3}{10}=\frac{131}{50}-\frac{15}{50}=\frac{116}{50}=2{,}32.$$

10. к)

    $$2{,}88\cdot\frac{35}{72}+\left(1{,}0625-\frac{5}{12}\right)\cdot 16$$
    $$=2\frac{88}{100}\cdot\frac{35}{72}+\left(1\frac{625}{10000}-\frac{5}{12}\right)\cdot 16$$
    $$=2\frac{22}{25}\cdot\frac{35}{72}+\left(1\frac{1}{16}-\frac{5}{12}\right)\cdot 16$$
    $$=\frac{72}{25}\cdot\frac{35}{72}+\left(1\frac{3}{48}-\frac{20}{48}\right)\cdot 16$$
    $$=\frac{7}{5}+\left(\frac{51}{48}-\frac{20}{48}\right)\cdot 16$$
    $$=\frac{7}{5}+\frac{31}{48}\cdot 16=\frac{7}{5}+\frac{31}{3}=1\frac{2}{5}+10\frac{1}{3}=11\frac{11}{15}.$$

Ответ

а) $$3$$; б) $$\frac{1}{4}$$; в) $$5{,}74$$; г) $$2$$; д) $$104$$; е) $$11{,}3$$; ж) $$64{,}5$$; з) $$1{,}225$$; и) $$2{,}32$$; к) $$11\frac{11}{15}$$.