Упражнение 2.463 - ГДЗ Математика 6 класс Виленкин

а) $\frac{4}{5}:1\frac{1}{3}+2\frac{1}{3}\cdot \frac{3}{7}-1:1\frac{3}{8}$

1. $\frac{4}{5}:1\frac{1}{3}=\frac{4}{5}:\frac{4}{3}=\frac{4}{5}\cdot \frac{3}{4}=\frac{3}{5}$

2. $2\frac{1}{3}\cdot \frac{3}{7}=\frac{7}{3}\cdot \frac{3}{7}=1$

3. $1:1\frac{3}{8}=1:\frac{11}{8}=\frac{8}{11}$

4. $\frac{3}{5}+1-\frac{8}{11}=1\frac{3}{5}-\frac{8}{11}=1\frac{33}{55}-\frac{40}{55}=\frac{88}{55}-\frac{40}{55}=\frac{48}{55}$

б) $2\frac{1}{6}:(1\frac{1}{15}-\frac{1}{5})+(2\frac{1}{8}+\frac{3}{4}):5\frac{3}{4}$

1. $1\frac{1}{15}-\frac{1}{5}=1\frac{1}{15}-\frac{3}{15}=\frac{16}{15}-\frac{3}{15}=\frac{13}{15}$

2. $2\frac{1}{6}:\frac{13}{15}=\frac{13}{6}\cdot \frac{15}{13}=\frac{15}{6}=2\frac{3}{6}=2\frac{1}{2}$

3. $2\frac{1}{8}+\frac{3}{4}=2\frac{1}{8}+\frac{6}{8}=2\frac{7}{8}$

4. $2\frac{7}{8}:5\frac{3}{4}=\frac{23}{8}:\frac{23}{4}=\frac{23}{8}\cdot \frac{4}{23}=\frac{1}{2}$

5. $2\frac{1}{2}+\frac{1}{2}=3$

в) $(\frac{1}{4}+1\frac{11}{14})\cdot \frac{14}{57}-\frac{2}{3}:1\frac{1}{6}\cdot \frac{7}{32}$

1. $\frac{1}{4}+1\frac{11}{14}=\frac{7}{28}+1\frac{22}{28}=1\frac{29}{28}=2\frac{1}{28}=\frac{57}{28}$

2. $\frac{57}{28}\cdot \frac{14}{57}=\frac{1}{2}$

3. $\frac{2}{3}:1\frac{1}{6}=\frac{2}{3}:\frac{7}{6}=\frac{2}{3}\cdot \frac{6}{7}=\frac{4}{7}$

4. $\frac{4}{7}\cdot \frac{7}{32}=\frac{4}{32}=\frac{1}{8}$

5. $\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{3}{8}$

г) $(2\frac{1}{2}:3\frac{1}{3}+3\frac{1}{3}:2\frac{1}{2})\cdot 9\frac{3}{5}$

1. $2\frac{1}{2}:3\frac{1}{3}=\frac{5}{2}:\frac{10}{3}=\frac{5}{2}\cdot \frac{3}{10}=\frac{3}{4}$

2. $3\frac{1}{3}:2\frac{1}{2}=\frac{10}{3}:\frac{5}{2}=\frac{10}{3}\cdot \frac{2}{5}=\frac{4}{3}$

3. $\frac{3}{4}+\frac{4}{3}=\frac{9}{12}+\frac{16}{12}=\frac{25}{12}$

4. $\frac{25}{12}\cdot 9\frac{3}{5}=\frac{25}{12}\cdot \frac{48}{5}=5\cdot 4=20$

д) $(10\frac{5}{13}-7\frac{23}{26}):\frac{5}{6}$

1. $10\frac{5}{13}-7\frac{23}{26}=10\frac{10}{26}-7\frac{23}{26}=9\frac{36}{26}-7\frac{23}{26}=2\frac{13}{26}=2\frac{1}{2}$

2. $2\frac{1}{2}:\frac{5}{6}=\frac{5}{2}:\frac{5}{6}=\frac{5}{2}\cdot \frac{6}{5}=3$

е) $((1\frac{1}{2}{)}^3-\frac{3}{4}):\frac{7}{8}$

1. $(1\frac{1}{2}{)}^3=(\frac{3}{2}{)}^3=\frac{27}{8}$

2. $\frac{27}{8}-\frac{3}{4}=\frac{27}{8}-\frac{6}{8}=\frac{21}{8}$

3. $\frac{21}{8}:\frac{7}{8}=\frac{21}{8}\cdot \frac{8}{7}=3$

Ответ: а) $\frac{48}{55}$; б) 3; в) $\frac{3}{8}$; г) 20; д) 3; е) 3.