Упражнение 880

Решение:

• $${\largeа)}\ 3\frac{2}{5}:x=6\frac{4}{5}:1\frac{1}{3}$$$$\phantom{\largeа)}\ \frac{17}{5}:x=\frac{34}{5}:\frac{4}{3}$$$$\phantom{\largeа)}\ x=\frac{17}{5}\cdot\frac{4}{3}:\frac{34}{5}$$$$\phantom{\largeа)}\ x=\frac{17}{5}\cdot\frac{4}{3}\cdot\frac{5}{34}$$$$\phantom{\largeа)}\ x=\frac{\cancel{17}^{\backslash1}\cdot4\cdot\cancel5^{\backslash1}}{\cancel5^{\backslash1}\cdot3\cdot\cancel{34}^{\backslash2}}$$$$\phantom{\largeа)}\ x=\frac{\cancel4^{\backslash2}}{3\cdot\cancel2^{\backslash1}}$$$$\phantom{\largeа)}\ x=\frac{2}{3}$$
• $${\largeб)}\ 7\frac{1}{3}:2\frac{1}{2}=3\frac{2}{3}:y$$$$\phantom{\largeб)}\ \frac{22}{3}:\frac{5}{2}=\frac{11}{3}:y$$$$\phantom{\largeб)}\ y=\frac{5}{2}\cdot\frac{11}{3}:\frac{22}{3}$$$$\phantom{\largeб)}\ y=\frac{5}{2}\cdot\frac{11}{3}\cdot\frac{3}{22}$$$$\phantom{\largeб)}\ y=\frac{5\cdot\cancel{11}^{\backslash1}\cdot\cancel3^{\backslash1}}{2\cdot\cancel3^{\backslash1}\cdot\cancel{22}^{\backslash2}}$$$$\phantom{\largeб)}\ y=\frac{5}{4}$$$$\phantom{\largeб)}\ y=1\frac{1}{4}$$
• $${\largeв)}\ 4\frac{2}{5}:x=8\frac{4}{5}:2\frac{1}{2}$$$$\phantom{\largeв)}\ \frac{22}{5}:x=\frac{44}{5}:\frac{5}{2}$$$$\phantom{\largeв)}\ x=\frac{22}{5}\cdot\frac{5}{2}:\frac{44}{5}$$$$\phantom{\largeв)}\ x=\frac{22}{5}\cdot\frac{5}{2}\cdot\frac{5}{44}$$$$\phantom{\largeв)}\ x=\frac{\cancel{22}^{\backslash1}\cdot\cancel5^{\backslash1}\cdot5}{\cancel5^{\backslash1}\cdot2\cdot\cancel{44}^{\backslash2}}$$$$\phantom{\largeв)}\ x=\frac{5}{4}$$$$\phantom{\largeв)}\ x=1\frac{1}{4}$$
• $${\largeг)}\ 6\frac{1}{2}:3\frac{3}{4}=3\frac{1}{4}:y$$$$\phantom{\largeг)}\ \frac{13}{2}:\frac{15}{4}=\frac{13}{4}:y$$$$\phantom{\largeг)}\ y=\frac{15}{4}\cdot\frac{13}{4}:\frac{13}{2}$$$$\phantom{\largeг)}\ y=\frac{15}{4}\cdot\frac{13}{4}\cdot\frac{2}{13}$$$$\phantom{\largeг)}\ y=\frac{15\cdot\cancel{13}^{\backslash1}\cdot\cancel2^{\backslash1}}{\cancel4^{\backslash2}\cdot4\cdot\cancel{13}^{\backslash1}}$$$$\phantom{\largeг)}\ y=\frac{15}{8}$$$$\phantom{\largeг)}\ y=1\frac{7}{8}$$