Упр.182 Часть 1 ГДЗ Дорофеев Петерсон 6 класс (Математика)

Задача

1) 4,5+0,5•(2,4•1,375-1,64:0,8) :2 1/12-1 2/7•1,4;
2) (2,5-0,75)•4/7+[(3 3/8-2 11/12)•1 7/9+2 11/12•1 7/9] :(3,5:2 1/3);
3) 0,198•9 1/11-[(2,56+3/4-2,56-0,125)•2 2/3-1/15] :16•(5 3/4+2,25);
4) (8,96:0,8+1 1/8•0,8) :1,1-[(5 7/12-2 17/36)•0,9-4 1/3 :2,6•0,6] :1/5.

Подробный ответ

1) $$4{,}5+0{,}5\cdot(2{,}4\cdot1{,}375-1{,}64:0{,}8):2\frac{1}{12}-1\frac{2}{7}\cdot1{,}4$$

$$2{,}4\cdot1{,}375=3{,}3$$

$$1{,}64:0{,}8=2{,}05$$

$$3{,}3-2{,}05=1{,}25$$

$$0{,}5\cdot1{,}25=0{,}625=\frac{5}{8}$$

$$2\frac{1}{12}=\frac{25}{12},\qquad \frac{5}{8}:\frac{25}{12}=\frac{5}{8}\cdot\frac{12}{25}=\frac{3}{10}=0{,}3$$

$$1\frac{2}{7}=\frac{9}{7},\qquad \frac{9}{7}\cdot1{,}4=\frac{9}{7}\cdot\frac{7}{5}=\frac{9}{5}=1{,}8$$

$$4{,}5+0{,}3-1{,}8=3$$

2) $$\left(2{,}5-0{,}75\right)\cdot\frac{4}{7}+\left[\left(3\frac{3}{8}-2\frac{11}{12}\right)\cdot1\frac{7}{9}+2\frac{11}{12}\cdot1\frac{7}{9}\right]:(3{,}5:2\frac{1}{3})$$

$$2{,}5-0{,}75=1{,}75=\frac{7}{4}$$

$$\frac{7}{4}\cdot\frac{4}{7}=1$$

$$3\frac{3}{8}=\frac{27}{8},\qquad 2\frac{11}{12}=\frac{35}{12},\qquad 1\frac{7}{9}=\frac{16}{9}$$

$$\left(\frac{27}{8}-\frac{35}{12}\right)\cdot\frac{16}{9}+\frac{35}{12}\cdot\frac{16}{9}=\frac{27}{8}\cdot\frac{16}{9}$$

$$\frac{27}{8}\cdot\frac{16}{9}=6$$

$$3{,}5:2\frac{1}{3}=\frac{7}{2}:\frac{7}{3}=\frac{3}{2}$$

$$6:\frac{3}{2}=4$$

$$1+4=5$$

3) $$0{,}198\cdot9\frac{1}{11}-\left[\left(2{,}56+\frac{3}{4}-2{,}56-0{,}125\right)\cdot2\frac{2}{3}-\frac{1}{15}\right]:16\cdot\left(5\frac{3}{4}+2{,}25\right)$$

$$9\frac{1}{11}=\frac{100}{11},\qquad 0{,}198=\frac{198}{1000}$$

$$0{,}198\cdot9\frac{1}{11}=\frac{198}{1000}\cdot\frac{100}{11}=\frac{9}{5}$$

$$2{,}56+\frac{3}{4}-2{,}56-0{,}125=\frac{3}{4}-\frac{1}{8}=\frac{5}{8}$$

$$2\frac{2}{3}=\frac{8}{3}$$

$$\frac{5}{8}\cdot\frac{8}{3}-\frac{1}{15}=\frac{5}{3}-\frac{1}{15}=\frac{24}{15}=\frac{8}{5}$$

$$5\frac{3}{4}+2{,}25=5{,}75+2{,}25=8$$

$$\frac{8}{5}-\left(\frac{8}{5}:16\cdot8\right)=\frac{8}{5}-\frac{1}{5}=1$$

4) $$\left(8{,}96:0{,}8+1\frac{1}{8}\cdot0{,}8\right):1{,}1-\left[\left(5\frac{7}{12}-2\frac{17}{36}\right)\cdot0{,}9-4\frac{1}{3}:2{,}6\cdot0{,}6\right]:\frac{1}{5}$$

$$8{,}96:0{,}8=11{,}2,\qquad 1\frac{1}{8}\cdot0{,}8=\frac{9}{8}\cdot\frac{8}{10}=0{,}9$$

$$11{,}2+0{,}9=12{,}1,\qquad 12{,}1:1{,}1=11$$

$$5\frac{7}{12}=\frac{67}{12},\qquad 2\frac{17}{36}=\frac{89}{36}$$

$$\frac{67}{12}-\frac{89}{36}=\frac{14}{9}$$

$$\frac{14}{9}\cdot0{,}9=\frac{14}{9}\cdot\frac{9}{10}=\frac{7}{5}$$

$$4\frac{1}{3}:2{,}6\cdot0{,}6=\frac{13}{3}:\frac{13}{5}\cdot\frac{3}{5}=1$$

$$\frac{7}{5}-1=\frac{2}{5}$$

$$\frac{2}{5}:\frac{1}{5}=2$$

$$11-2=9$$