Bài 2:
1)
\(-\frac{6}{9}=\frac{4}{x}=\frac{y}{-12}=\frac{z}{-15}\\ \Leftrightarrow\left(-\frac{6}{9}=\frac{4}{x}\right)\Rightarrow x=\frac{4\cdot9}{-6}=-6\\ \Leftrightarrow\left(-\frac{6}{9}=\frac{y}{12}\right)\Rightarrow y=\frac{12\cdot6}{-9}=-8\\ \Leftrightarrow\left(-\frac{6}{9}=\frac{z}{-15}\right)\Rightarrow z=\frac{-15\cdot-6}{9}=10\)
2)
\(\frac{x}{16}=\frac{y}{-32}=-\frac{8}{z}=\frac{7}{8}\\ \Leftrightarrow\left(\frac{x}{16}=\frac{7}{8}\right)\Rightarrow x=\frac{16\cdot7}{8}=14\\ \Leftrightarrow\left(\frac{y}{-32}=\frac{7}{8}\right)\Rightarrow y=\frac{7\cdot-32}{8}=-28\\ \Leftrightarrow\left(-\frac{8}{z}=\frac{7}{8}\right)\Rightarrow z=\frac{-8\cdot8}{7}=-\frac{64}{7}\)
3)
\(\frac{x}{-5}=\frac{6}{y}=-\frac{14}{z}=-\frac{8}{20}\\ \Leftrightarrow\left(\frac{x}{-5}=-\frac{8}{20}\right)\Rightarrow x=\frac{-5\cdot-8}{20}=2\\ \Leftrightarrow\left(\frac{6}{y}=-\frac{8}{20}\right)\Rightarrow y=\frac{6\cdot20}{-8}=-15\\ \Leftrightarrow\left(-\frac{14}{z}=-\frac{8}{20}\right)\Rightarrow z=\frac{-14\cdot-20}{8}=35\)
4)
\(\frac{x}{-18}=\frac{y}{36}=-\frac{20}{z}=-\frac{5}{9}\\ \Leftrightarrow\left(\frac{x}{-18}=-\frac{5}{9}\right)\Rightarrow x=\frac{-18\cdot-5}{9}=10\\ \Leftrightarrow\left(\frac{y}{36}=-\frac{5}{9}\right)\Rightarrow y=\frac{36\cdot-5}{9}=-20\\ \Leftrightarrow\left(-\frac{20}{z}=-\frac{5}{9}\right)\Rightarrow z=\frac{-9\cdot-20}{5}=36\)
5)
\(-\frac{6}{9}=-\frac{8}{x}=\frac{y}{-36}=\frac{z}{12}\\ \Leftrightarrow\left(-\frac{6}{9}=-\frac{8}{x}\right)\Rightarrow x=\frac{-8\cdot-9}{6}=12\\ \Leftrightarrow\left(-\frac{6}{9}=\frac{y}{-36}\right)\Rightarrow y=\frac{-6\cdot-36}{9}=24\\ \Leftrightarrow\left(-\frac{6}{9}=\frac{z}{12}\right)\Rightarrow z=\frac{12\cdot-6}{9}=-8\)
6)
\(\frac{x}{-8}=\frac{y}{40}=-\frac{24}{z}=-\frac{7}{8}\\ \Leftrightarrow\left(\frac{x}{-8}=-\frac{7}{8}\right)\Rightarrow x=\frac{-7\cdot-8}{8}=7\\ \Leftrightarrow\left(\frac{y}{40}=-\frac{7}{8}\right)\Rightarrow y=\frac{-7\cdot40}{8}=-35\\ \Leftrightarrow\left(-\frac{24}{z}=-\frac{7}{8}\right)\Rightarrow z=\frac{-24\cdot-8}{7}=\frac{192}{7}\)
Bài 3
1) \(3\cdot81=9\cdot27\)
\(\frac{3}{9}=\frac{27}{81};\frac{9}{3}=\frac{81}{27};\frac{9}{81}=\frac{3}{27};\frac{81}{9}=\frac{27}{3}\)
2) \(2\cdot14=4\cdot7\)
\(\frac{2}{4}=\frac{7}{14};\frac{4}{2}=\frac{14}{7};\frac{4}{14}=\frac{2}{7};\frac{14}{4}=\frac{7}{2}\)
3) \(4\cdot15=5\cdot12\)
\(\frac{4}{5}=\frac{12}{15};\frac{5}{4}=\frac{15}{12};\frac{5}{15}=\frac{4}{12};\frac{15}{5}=\frac{12}{4}\)
4) \(20\cdot6=5\cdot24\)
\(\frac{5}{20}=\frac{6}{24};\frac{20}{5}=\frac{24}{6};\frac{5}{6}=\frac{20}{24};\frac{6}{5}=\frac{24}{20}\)
