Упр.15.17 ГДЗ Рабочая тетрадь Зубарева Мордкович 6 класс Экзамен (Математика)

Задача

а) 2/5 x=5 3/5;
б) a:2 1/2=3 1/3•1/3;
в) 2/9 x+5/9 x=11 2/3;
г) 5 1/3•(3/5 x+1/8)=1 2/3;
д) 7/12 :x=3/20 :3/10;
е) (5 7/18-4 23/30) :(1,12•1 1/9)=x:(3,2+0,8•(5 1/2-3,25));
ж) (10,5•0,24-15,15:7,5) :x=(3 5/24-2 7/30) :(1 11/15•3/8).

Подробный ответ

а) $$\frac{2}{5}x=5\frac{3}{5}$$

$$5\frac{3}{5}=\frac{28}{5}$$

$$x=\frac{28}{5}:\frac{2}{5}=\frac{28}{5}\cdot\frac{5}{2}=14$$

б) $$a:2\frac{1}{2}=3\frac{1}{3}\cdot\frac{1}{3}$$

$$2\frac{1}{2}=\frac{5}{2}, \quad 3\frac{1}{3}=\frac{10}{3}$$

$$a:\frac{5}{2}=\frac{10}{3}\cdot\frac{1}{3}=\frac{10}{9}$$

$$a=\frac{10}{9}\cdot\frac{5}{2}=\frac{25}{9}=2\frac{7}{9}$$

в) $$\frac{2}{9}x+\frac{5}{9}x=11\frac{2}{3}$$

$$\frac{7}{9}x=11\frac{2}{3}=\frac{35}{3}$$

$$x=\frac{35}{3}:\frac{7}{9}=\frac{35}{3}\cdot\frac{9}{7}=15$$

г) $$5\frac{1}{3}\left(\frac{3}{5}x+\frac{1}{8}\right)=1\frac{2}{3}$$

$$5\frac{1}{3}=\frac{16}{3}, \quad 1\frac{2}{3}=\frac{5}{3}$$

$$\frac{16}{3}\left(\frac{3}{5}x+\frac{1}{8}\right)=\frac{5}{3}$$

$$\frac{16}{5}x+\frac{16}{3}\cdot\frac{1}{8}=\frac{5}{3}$$

$$\frac{16}{5}x+\frac{2}{3}=\frac{5}{3}$$

$$\frac{16}{5}x=\frac{5}{3}-\frac{2}{3}=1$$

$$x=1:\frac{16}{5}=\frac{5}{16}$$

д) $$\frac{7}{12}:x=\frac{3}{20}:\frac{3}{10}$$

$$\frac{3}{20}:\frac{3}{10}=\frac{3}{20}\cdot\frac{10}{3}=\frac{1}{2}$$

$$\frac{7}{12}:x=\frac{1}{2}$$

$$x=\frac{7}{12}:\frac{1}{2}=\frac{7}{12}\cdot 2=\frac{7}{6}=1\frac{1}{6}$$

е) $$\left(5\frac{7}{18}-4\frac{23}{30}\right):\left(1{,}12\cdot1\frac{1}{9}\right)=x:\left(3{,}2+0{,}8\cdot\left(5\frac{1}{2}-3{,}25\right)\right)$$

$$5\frac{7}{18}=\frac{97}{18}, \quad 4\frac{23}{30}=\frac{143}{30}$$

$$\frac{97}{18}-\frac{143}{30}=\frac{485-429}{90}=\frac{56}{90}=\frac{28}{45}$$

$$1{,}12\cdot1\frac{1}{9}=\frac{112}{100}\cdot\frac{10}{9}=\frac{112}{90}=\frac{56}{45}$$

$$\left(5\frac{7}{18}-4\frac{23}{30}\right):\left(1{,}12\cdot1\frac{1}{9}\right)=\frac{28}{45}:\frac{56}{45}=\frac{1}{2}$$

$$5\frac{1}{2}-3{,}25=5{,}5-3{,}25=2{,}25$$

$$0{,}8\cdot2{,}25=1{,}8$$

$$3{,}2+1{,}8=5$$

Тогда $$\frac{1}{2}=x:5$$, значит

$$x=\frac{1}{2}\cdot 5=2{,}5$$

ж) $$\left(10{,}5\cdot0{,}24-15{,}15:7{,}5\right):x=\left(3\frac{5}{24}-2\frac{7}{30}\right):\left(1\frac{11}{15}\cdot\frac{3}{8}\right)$$

$$10{,}5\cdot0{,}24=2{,}52,\quad 15{,}15:7{,}5=2{,}02$$

$$2{,}52-2{,}02=0{,}5=\frac{1}{2}$$

$$3\frac{5}{24}-2\frac{7}{30}=\frac{77}{24}-\frac{67}{30}=\frac{385-268}{120}=\frac{117}{120}=\frac{39}{40}$$

$$1\frac{11}{15}\cdot\frac{3}{8}=\frac{26}{15}\cdot\frac{3}{8}=\frac{13}{20}$$

$$\left(3\frac{5}{24}-2\frac{7}{30}\right):\left(1\frac{11}{15}\cdot\frac{3}{8}\right)=\frac{39}{40}:\frac{13}{20}=\frac{39}{40}\cdot\frac{20}{13}=\frac{3}{2}$$

Тогда $$\frac{1}{2}:x=\frac{3}{2}$$, значит

$$x=\frac{1}{2}:\frac{3}{2}=\frac{1}{2}\cdot\frac{2}{3}=\frac{1}{3}$$