Задание 105 Вариант 1 Самостоятельная работа ГДЗ Дидактические материалы Чесноков 6 класс (Математика)

а) $$3\frac{3}{7}+1\frac{3}{14}\cdot\left(8\frac{3}{5}-1\frac{3}{5}\right)=11\frac{13}{14}$$

$$8\frac{3}{5}-1\frac{3}{5}=7$$

$$1\frac{3}{14}\cdot 7=\frac{17}{14}\cdot 7=\frac{17}{2}=8\frac{1}{2}$$

$$3\frac{3}{7}+8\frac{1}{2}=3\frac{6}{14}+8\frac{7}{14}=11\frac{13}{14}$$

б) $$2\frac{5}{9}\cdot 2\frac{1}{4}-6\frac{2}{9}: \frac{3}{8}=3\frac{5}{12}$$

$$2\frac{5}{9}\cdot 2\frac{1}{4}=\frac{23}{9}\cdot \frac{9}{4}=\frac{23}{4}=5\frac{3}{4}$$

$$6\frac{2}{9}:\frac{3}{8}=\frac{56}{9}\cdot \frac{8}{3}=\frac{56\cdot 8}{9\cdot 3}=\frac{7}{3}=2\frac{1}{3}$$

$$5\frac{3}{4}-2\frac{1}{3}=5\frac{9}{12}-2\frac{4}{12}=3\frac{5}{12}$$

в) $$\left(6\frac{2}{5}\cdot 2\frac{11}{12}-2\cdot 16\right):3\frac{1}{4}=6$$

$$6\frac{2}{5}\cdot 2\frac{11}{12}=\frac{32}{5}\cdot \frac{35}{12}=\frac{8\cdot 7}{1\cdot 3}=\frac{56}{3}=18\frac{2}{3}$$

$$18\frac{2}{3}-16=2\frac{2}{3}$$

$$2\frac{2}{3}:2\frac{1}{4}=\frac{8}{3}:\frac{9}{4}=\frac{8}{3}\cdot \frac{4}{9}=\frac{32}{27}=6$$

г) $$\left(\frac{1}{2}\right)^3\cdot \left(3\frac{1}{3}-2\frac{8}{9}\right)^2=\frac{2}{81}$$

$$\left(\frac{1}{2}\right)^3=\frac{1}{8}$$

$$3\frac{1}{3}-2\frac{8}{9}=3\frac{3}{9}-2\frac{8}{9}=2\frac{12}{9}-2\frac{8}{9}=\frac{4}{9}$$

$$\left(\frac{4}{9}\right)^2=\frac{16}{81}$$

$$\frac{1}{8}\cdot \frac{16}{81}=\frac{2}{81}$$

д) $$\left(3\frac{2}{3}-2\frac{1}{2}\right)\cdot 2\frac{1}{7}-3\frac{1}{2}=1$$

$$3\frac{2}{3}-2\frac{1}{2}=3\frac{4}{6}-2\frac{3}{6}=1\frac{1}{6}$$

$$1\frac{1}{6}\cdot 2\frac{1}{7}=\frac{7}{6}\cdot \frac{15}{7}=\frac{5}{2}=2\frac{1}{2}$$

$$2\frac{1}{2}-3\frac{1}{2}=1$$

е) $$12\cdot \left(\frac{11}{12}-\frac{9}{10}\right)\cdot \left(3-1\frac{1}{3}\right)=\frac{1}{3}$$

$$\frac{11}{12}-\frac{9}{10}=\frac{55}{60}-\frac{54}{60}=\frac{1}{60}$$

$$3-1\frac{1}{3}=2\frac{3}{3}-1\frac{1}{3}=1\frac{2}{3}$$

$$12\cdot \frac{1}{60}=\frac{1}{5}$$

$$\frac{1}{5}\cdot 1\frac{2}{3}=\frac{1}{5}\cdot \frac{5}{3}=\frac{1}{3}$$

Ответ: а) $$11\frac{13}{14}$$; б) $$3\frac{5}{12}$$; в) $$6$$; г) $$\frac{2}{81}$$; д) $$1$$; е) $$\frac{1}{3}$$.