Упр.181 Часть 1 ГДЗ Дорофеев Петерсон 6 класс (Математика)

Задача

1) (1,5:1/3-3/8 :0,25)•3,2-3,2•5/8;
2) 7/40 :2 11/12-0,1•(1,45:2 1/3-1/20 :2 1/3);
3) (3,6•2 7/9+1,125+5 2/5•2 7/9-1 1/8) :2,5;
4) 20:33 1/3-(4 7/25-1,28) :(0,75+3 1/4)•0,2.

Подробный ответ

1) $$\left(1{,}5: \frac13-\frac38:0{,}25\right)\cdot 3{,}2-3{,}2\cdot \frac58$$

$$1{,}5:\frac13=1{,}5\cdot 3=4{,}5$$
$$\frac38:0{,}25=\frac38:\frac14=\frac38\cdot 4=1{,}5$$
$$4{,}5-1{,}5=3$$
$$3\cdot 3{,}2-3{,}2\cdot \frac58=3{,}2\left(3-\frac58\right)=3{,}2\cdot \frac{19}{8}=7{,}6$$

2) $$\frac{7}{40}:2\frac{11}{12}-0{,}1\cdot \left(1{,}45:2\frac13-\frac1{20}:2\frac13\right)$$

$$1{,}45:2\frac13=\frac{145}{100}:\frac73=\frac{145}{100}\cdot \frac37=\frac{87}{140}$$
$$\frac1{20}:2\frac13=\frac1{20}:\frac73=\frac1{20}\cdot \frac37=\frac{3}{140}$$
$$\frac{87}{140}-\frac{3}{140}=\frac{84}{140}=\frac35=0{,}6$$
$$0{,}1\cdot 0{,}6=0{,}06$$
$$\frac{7}{40}:2\frac{11}{12}=\frac{7}{40}:\frac{35}{12}=\frac{7}{40}\cdot \frac{12}{35}=\frac{3}{50}=0{,}06$$
$$0{,}06-0{,}06=0$$

3) $$\left(3{,}6\cdot 2\frac79+1{,}125+5\frac25\cdot 2\frac79-1\frac18\right):2{,}5$$

$$3{,}6\cdot 2\frac79+5\frac25\cdot 2\frac79=\left(3{,}6+5\frac25\right)\cdot 2\frac79$$
$$1{,}125-1\frac18=1{,}125-1{,}125=0$$
$$3{,}6+5\frac25=3{,}6+5{,}4=9$$
$$9\cdot 2\frac79=9\cdot \frac{25}{9}=25$$
$$25:2{,}5=10$$

4) $$20:33\frac13-\left(4\frac7{25}-1{,}28\right):\left(0{,}75+3\frac14\right)\cdot 0{,}2$$

$$4\frac7{25}-1{,}28=4{,}28-1{,}28=3$$
$$0{,}75+3\frac14=0{,}75+3{,}25=4$$
$$20:33\frac13=20:\frac{100}{3}=20\cdot \frac3{100}=\frac35$$
$$3:4=\frac34$$
$$\frac34\cdot 0{,}2=\frac34\cdot \frac15=\frac3{20}$$
$$\frac35-\frac3{20}=\frac{12}{20}-\frac3{20}=\frac9{20}=0{,}45$$