Упр.848 ГДЗ Никольский Потапов 7 класс (Алгебра)

б) (3*5/18 — 7*1/12 + 2*2/9)*(2,448 :1,2);
в) (5/9-1*1/6*0,5):5/9-1/3;
г) 1/3*(0,216:0,2-0,12*10);
д) (2,4*0,5-2:1/2):0,1;
е) 3,6:(68,1:7,5-8*17/20 + 2*1/50)+4*5/6*33/58;
ж) 0,3 — 4,2:(2,25-1*7/8*3*1/3).

1. а)

   $$\frac{5}{12}:\left(\frac{1}{3}\cdot 2{,}5-\frac{7}{8}\right)-1{,}25= \frac{5}{12}:\left(\frac{5}{6}-\frac{7}{8}\right)-1{,}25$$

   $$\frac{5}{6}-\frac{7}{8}=\frac{20-21}{24}=-\frac{1}{24}$$

   $$\frac{5}{12}:\left(-\frac{1}{24}\right)-1{,}25=\frac{5}{12}\cdot(-24)-1{,}25=-10-1{,}25=-11{,}25$$

2. б)

   $$ \left(3\cdot \frac{5}{18}-7\cdot \frac{1}{12}+2\cdot \frac{2}{9}\right)\cdot (2{,}448:1{,}2) $$

   $$ 3\cdot \frac{5}{18}=\frac{5}{6},\quad 7\cdot \frac{1}{12}=\frac{7}{12},\quad 2\cdot \frac{2}{9}=\frac{4}{9},\quad 2{,}448:1{,}2=2{,}04 $$

   $$ \frac{5}{6}-\frac{7}{12}+\frac{4}{9} =\frac{30-21+16}{36} =\frac{25}{36} $$

   $$ \frac{25}{36}\cdot 2{,}04=\frac{25}{36}\cdot \frac{51}{25}=\frac{51}{36}=1{,}416\ldots $$

   $$\text{Тогда } \left(3\cdot \frac{5}{18}-7\cdot \frac{1}{12}+2\cdot \frac{2}{9}\right)\cdot (2{,}448:1{,}2)=1{,}416\ldots$$

3. в)

   $$\left(\frac{5}{9}-1\cdot \frac{1}{6}\cdot 0{,}5\right):\frac{5}{9}-\frac{1}{3}$$

   $$1\cdot \frac{1}{6}\cdot 0{,}5=\frac{1}{12}$$

   $$ \left(\frac{5}{9}-\frac{1}{12}\right):\frac{5}{9}-\frac{1}{3} =\frac{20-3}{36}:\frac{5}{9}-\frac{1}{3} =\frac{17}{36}\cdot \frac{9}{5}-\frac{1}{3} =\frac{17}{20}-\frac{1}{3} $$

   $$ \frac{17}{20}-\frac{1}{3}=\frac{51-20}{60}=\frac{31}{60} $$

4. г)

   $$\frac{1}{3}\cdot (0{,}216:0{,}2-0{,}12\cdot 10)$$

   $$0{,}216:0{,}2=1{,}08,\quad 0{,}12\cdot 10=1{,}2$$

   $$\frac{1}{3}\cdot (1{,}08-1{,}2)=\frac{1}{3}\cdot (-0{,}12)=-0{,}04$$

5. д)

   $$\left(2{,}4\cdot 0{,}5-2:\frac{1}{2}\right):0{,}1$$

   $$2{,}4\cdot 0{,}5=1{,}2,\quad 2:\frac{1}{2}=4$$

   $$\left(1{,}2-4\right):0{,}1=-2{,}8:0{,}1=-28$$

6. е)

   $$3{,}6:(68{,}1:7{,}5-8\cdot \frac{17}{20}+2\cdot \frac{1}{50})+4\cdot \frac{5}{6}\cdot \frac{33}{58}$$

   $$68{,}1:7{,}5=9{,}08,\quad 8\cdot \frac{17}{20}=6{,}8,\quad 2\cdot \frac{1}{50}=0{,}04$$

   $$9{,}08-6{,}8+0{,}04=2{,}32$$

   $$3{,}6:2{,}32+\;4\cdot \frac{5}{6}\cdot \frac{33}{58}$$

   $$3{,}6:2{,}32=\frac{360}{232}=\frac{45}{29},\qquad 4\cdot \frac{5}{6}\cdot \frac{33}{58}=\frac{55}{29}$$

   $$\frac{45}{29}+\frac{55}{29}=\frac{100}{29}$$

7. ж)

   $$0{,}3-4{,}2:(2{,}25-1\cdot \frac{7}{8}\cdot 3\cdot \frac{1}{3})$$

   $$1\cdot \frac{7}{8}\cdot 3\cdot \frac{1}{3}=\frac{7}{8}$$

   $$2{,}25-\frac{7}{8}=2{,}25-0{,}875=1{,}375$$

   $$4{,}2:1{,}375=\frac{42}{10}:\frac{11}{8}=\frac{42}{10}\cdot \frac{8}{11}=\frac{168}{55}$$

   $$0{,}3-\frac{168}{55}=-\frac{321}{110}=-2{,}91818\ldots$$

Ответ

а) $$-11{,}25$$; б) $$1{,}416\ldots$$; в) $$\frac{31}{60}$$; г) $$-0{,}04$$; д) $$-28$$; е) $$\frac{100}{29}$$; ж) $$-\frac{321}{110}$$.