Упр.522 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) (5,4·1,2-3,7:0,8)(3,14+0,86):0,25;
2) (20,88:18+45:0,36):(19,59+11,95);
3) (5 8/9-3 11/12)·18/71-7 5/6:15 2/3;
4) 7/36·9+8·11/32+9/10·5/18.

1. $$\left(5{,}4\cdot 1{,}2-3{,}7:0{,}8\right)\left(3{,}14+0{,}86\right):0{,}25$$

   $$5{,}4\cdot 1{,}2=6{,}48,\qquad 3{,}7:0{,}8=4{,}625,\qquad 3{,}14+0{,}86=4$$

   $$\left(6{,}48-4{,}625\right)\cdot 4:0{,}25=1{,}855\cdot 4\cdot 4=29{,}68$$

   $$29{,}68=\frac{742}{25}=29\frac{17}{25}$$

2. $$\left(20{,}88:18+45:0{,}36\right):\left(19{,}59+11{,}95\right)$$

   $$20{,}88:18=1{,}16,\qquad 45:0{,}36=125,\qquad 19{,}59+11{,}95=31{,}54$$

   $$\left(1{,}16+125\right):31{,}54=126{,}16:31{,}54=4$$

3. $$\left(5\frac{8}{9}-3\frac{11}{12}\right)\cdot \frac{18}{71}-7\frac{5}{6}:15\frac{2}{3}$$

   $$5\frac{8}{9}=\frac{53}{9},\qquad 3\frac{11}{12}=\frac{47}{12},\qquad 7\frac{5}{6}=\frac{47}{6},\qquad 15\frac{2}{3}=\frac{47}{3}$$

   $$\left(\frac{53}{9}-\frac{47}{12}\right)\cdot \frac{18}{71}-\frac{47}{6}:\frac{47}{3}$$

   $$\frac{53}{9}-\frac{47}{12}=\frac{212-141}{36}=\frac{71}{36}$$

   $$\frac{71}{36}\cdot \frac{18}{71}=\frac{1}{2},\qquad \frac{47}{6}:\frac{47}{3}=\frac{47}{6}\cdot \frac{3}{47}=\frac{1}{2}$$

   $$\frac{1}{2}-\frac{1}{2}=0$$

4. $$\frac{7}{36}\cdot 9+8\cdot \frac{11}{32}+\frac{9}{10}\cdot \frac{5}{18}$$

   $$\frac{7}{36}\cdot 9=\frac{7}{4},\qquad 8\cdot \frac{11}{32}=\frac{11}{4},\qquad \frac{9}{10}\cdot \frac{5}{18}=\frac{1}{4}$$

   $$\frac{7}{4}+\frac{11}{4}+\frac{1}{4}=\frac{19}{4}=4{,}75$$

Ответ

1) $$29\frac{17}{25}$$; 2) $$4$$; 3) $$0$$; 4) $$4{,}75$$.