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1 a) \(\dfrac{\left(-2\right)}{5}\)= \(\dfrac{-6}{15}\); \(\dfrac{15}{-6}\)= \(\dfrac{5}{-2}\); \(\dfrac{-6}{-2}\)= \(\dfrac{15}{5}\); \(\dfrac{-2}{-6}\)= \(\dfrac{5}{15}\)
1)
a) \(1\dfrac{5}{6}=\dfrac{-x}{5}\)
\(\Rightarrow\dfrac{11}{6}=\dfrac{-x}{5}\)
\(\Rightarrow-x=\dfrac{5.11}{6}=\dfrac{55}{6}\)
\(\Rightarrow x=-\dfrac{55}{6}\)
b) 4,25 : 8 = -3,5 : x
\(\dfrac{4,25}{8}=\dfrac{-3,5}{x}\)
\(x=\dfrac{-3,5.8}{4,25}\)
\(x=\dfrac{-28}{4,25}\)
2.
\(-\dfrac{12}{1,6}=\dfrac{55}{-7\dfrac{1}{3}}\)
\(\Rightarrow-\dfrac{12}{1,6}=\dfrac{55}{-\dfrac{22}{3}}\)
Ta có thể lặp đc các tỉ lệ thức sau:
\(-\dfrac{12}{1,6}=\dfrac{55}{-\dfrac{22}{3}}\)
\(\dfrac{-\dfrac{22}{3}}{1,6}=\dfrac{55}{-12}\)
\(-\dfrac{12}{55}=\dfrac{1,6}{-\dfrac{22}{3}}\)
\(\dfrac{1,6}{-12}=\dfrac{-\dfrac{22}{3}}{55}\)
6:(-27)=(\(-6\dfrac{1}{2}\))\(:29\dfrac{1}{4}\)
\(\Leftrightarrow\)6:(-27)=\(\left(-\dfrac{13}{2}\right):\dfrac{117}{4}\)
\(\Rightarrow\)\(\left(-\dfrac{13}{2}\right):\dfrac{117}{4}\)=\(\left(-\dfrac{13}{2}\right):\dfrac{4}{117}\)=\(-\dfrac{2}{9}\)
Ta có:\(\dfrac{6}{-27}=\dfrac{-2}{9}\)
hay\(\dfrac{6}{-2}=\dfrac{-27}{9}\);\(\dfrac{6}{-2}=\dfrac{27}{-9}\);\(\dfrac{2}{-9}=\dfrac{6}{-27}\)
\(\dfrac{6}{-6,5}=\dfrac{29,25}{-27};\dfrac{6,5}{6}=\dfrac{-27}{29,25}\)
\(Từ\) \(\dfrac{-1,2}{1,6}=\dfrac{55}{-7\dfrac{1}{3}}\Rightarrow\) \(\dfrac{1,6}{-1,2}=\dfrac{-7\dfrac{1}{3}}{55}\)
\(\Rightarrow\dfrac{-7\dfrac{1}{3}}{55}=\dfrac{1,6}{-1,2}\)
\(\Rightarrow\dfrac{55}{-7\dfrac{1}{3}}=\dfrac{-1,2}{1,6}\)
Bài 1:
Ta có:
+) \(3.4=2.6\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{3}{2}=\dfrac{6}{4}\\\dfrac{3}{6}=\dfrac{2}{4}\\\dfrac{4}{2}=\dfrac{6}{3}\\\dfrac{4}{6}=\dfrac{2}{3}\end{matrix}\right.\)
+) \(3.6=2.9\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{3}{2}=\dfrac{9}{6}\\\dfrac{3}{9}=\dfrac{2}{6}\\\dfrac{6}{2}=\dfrac{9}{3}\\\dfrac{6}{9}=\dfrac{2}{3}\end{matrix}\right.\)
Bài 2:
a) Ta có: \(\dfrac{x}{11}=\dfrac{y}{13}\) và \(x-y=6\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{11}=\dfrac{y}{13}=\dfrac{x-y}{11-13}=\dfrac{6}{-2}=-3\)
\(\Rightarrow\left\{{}\begin{matrix}x=11.\left(-3\right)=-33\\y=13.\left(-3\right)=-39\end{matrix}\right.\)
Vậy \(x=-33;y=-39\)
b) Theo bài ra ta có:
\(x:y:z=1:2:3\)
\(\Rightarrow\dfrac{x}{1}=\dfrac{y}{2}=\dfrac{z}{3}\)
\(\Rightarrow\dfrac{4x}{4}=\dfrac{3y}{6}=\dfrac{2z}{6}\)
và \(4x-3y+2z=36\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{4x}{4}=\dfrac{3y}{6}=\dfrac{2z}{6}=\dfrac{4x-3y+2z}{4-6+6}=\dfrac{36}{4}=9\)
\(\Rightarrow\left\{{}\begin{matrix}4x=4.9=36\Rightarrow x=9\\3y=6.9=54\Rightarrow y=18\\2z=6.9=54\Rightarrow z=27\end{matrix}\right.\)
Vậy \(x=9;y=18;z=27\)
c) Ta có: \(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{-2}\)
\(\Rightarrow\dfrac{5x}{15}=\dfrac{y}{5}=\dfrac{3z}{-6}\)
và \(5x-y+3z=124\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{5x}{15}=\dfrac{y}{5}=\dfrac{3z}{-6}=\dfrac{5x-y+3z}{15-5+\left(-6\right)}=\dfrac{124}{4}=31\)
\(\Rightarrow\left\{{}\begin{matrix}5x=15.31=465\Rightarrow x=93\\y=5.31=155\\3z=\left(-6\right).31=-186\Rightarrow z=-62\end{matrix}\right.\)
Vậy \(x=93;y=155;z=-62\)
a: Vì \(2.8\cdot0.4=1.4\cdot0.8\)
nên 2,8/0,8=1,4/0,4; 2,8/1,4=0,8/0,4; 0,8/2,8=0,4/1,4; 1,4/2,8=0,4/0,8
b: Vì x,y,z tỉ lệ với 3;5;6 nên x/3=y/5=z/6=k
=>x=3k; y=5k; z=6k
\(M=\dfrac{2x-3y+4z}{x-11y-4z}=\dfrac{6k-15k+24k}{3k-55k-24k}=\dfrac{-15}{76}\)
a) \(\dfrac{x}{3}=\dfrac{y}{5}\) và x + y = 16
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{x+y}{3+5}=\dfrac{16}{8}=2\)
\(\dfrac{x}{3}\Rightarrow x=3.2=6\)
\(\dfrac{y}{5}\Rightarrow y=5.2=10\)
=> x = 6
y = 10
\(\dfrac{x}{7}=\dfrac{6}{y}\\ \Rightarrow\dfrac{x}{6}=\dfrac{7}{y}\\ \Rightarrow\dfrac{6}{x}=\dfrac{y}{7}\\ \Rightarrow\dfrac{7}{x}=\dfrac{y}{6}\)