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1 a) \(\dfrac{\left(-2\right)}{5}\)= \(\dfrac{-6}{15}\); \(\dfrac{15}{-6}\)= \(\dfrac{5}{-2}\); \(\dfrac{-6}{-2}\)= \(\dfrac{15}{5}\); \(\dfrac{-2}{-6}\)= \(\dfrac{5}{15}\)
a, \(2,5:7,5=x:\dfrac{3}{5}\)
\(\Leftrightarrow x:\dfrac{3}{5}=2,5:7,5\)
=> \(x.7,5=\dfrac{3}{5}.2,5\) => \(x=\dfrac{1,5}{7,5}=\dfrac{1}{5}\)
b, \(2\dfrac{2}{3}:x=1\dfrac{7}{9}\)
=> \(x=2\dfrac{2}{3}:1\dfrac{7}{9}\)
=> \(x=\dfrac{3}{2}\)
c, \(\dfrac{5}{6}:x=20:3\)
=> \(x.20=\dfrac{5}{6}.3\) => \(x=\dfrac{2,5}{20}=\dfrac{1}{8}\)
3, Tìm x, biết:
a) 2,5 : 7,5 = x : \(\dfrac{3}{5}\)
=> \(x:\dfrac{3}{5}=\dfrac{1}{3}\)
=> \(x=\dfrac{1}{3}.\dfrac{3}{5}=>x=\dfrac{1}{5}\)
b) \(2\dfrac{2}{3}\) : x = \(1\dfrac{7}{9}\)
=> \(\dfrac{8}{3}:x=\dfrac{16}{9}\)
=> \(x=\dfrac{8}{3}:\dfrac{16}{9}=>x=\dfrac{3}{2}\)
c) \(\dfrac{5}{6}\) : x = 20 : 3
=> \(x=\dfrac{5}{6}:\dfrac{20}{3}=>x=\dfrac{1}{8}\)
Mấy bài dễ tự làm nhé:D
1)
Đặt: \(\dfrac{a}{b}=\dfrac{c}{d}=k\Leftrightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{a}{a+b}=\dfrac{bk}{bk+b}=\dfrac{bk}{b\left(k+1\right)}=\dfrac{k}{k+1}\\\dfrac{c}{c+d}=\dfrac{dk}{dk+d}=\dfrac{dk}{d\left(k+1\right)}=\dfrac{k}{k+1}\end{matrix}\right.\)
Ta có điều phải chứng minh
\(\left\{{}\begin{matrix}\dfrac{a}{a-b}=\dfrac{bk}{bk-b}=\dfrac{bk}{b\left(k-1\right)}=\dfrac{k}{k-1}\\\dfrac{c}{c-d}=\dfrac{dk}{dk-d}=\dfrac{dk}{d\left(k-1\right)}=\dfrac{k}{k-1}\end{matrix}\right.\)
Ta có điều phải chứng minh
Cái này chỉ cần làm quy tắc nhân chéo là ra rồi nhé :)
a) \(x=\dfrac{-2,6.42}{-12}\)=9,1
b) x = \(\dfrac{2,5.12}{1.5}\) = 20
c) Nhân chéo: 7.(x-1) = 6.(x+5)
<=> 7x - 7 = 6x +30
<=> 7x - 6x = 7 + 30 (chuyển vế)
-> x = 37
d) Nhân chéo: 25x2 = 24.6 = 144
x2 = \(\dfrac{144}{25}\)=5,76
-> x = \(\sqrt{5,76}\) = 2,4
e) Nhân chéo: (x-2)2 = 4.9 = 36
Ta dễ thấy (x-2)2 = 62
-> x-2 = 6 -> x = 6+2 = 8
TICK NHÉ :)
2.
a) \(\dfrac{x-1}{4}=\dfrac{9}{x-1}\)
\(\Leftrightarrow\left(x-1\right)^2=9.4\)
\(\Leftrightarrow\left(x-1\right)^2=36\)
\(\Leftrightarrow\left(x-1\right)^2=\left[{}\begin{matrix}6^2\\-6^2\end{matrix}\right.\)
\(\Leftrightarrow x-1=\left[{}\begin{matrix}6\\-6\end{matrix}\right.\)
\(\Leftrightarrow x=\left[{}\begin{matrix}7\\-5\end{matrix}\right.\)
1. a. \(\dfrac{3}{-1}=\dfrac{-15}{5}\); \(\dfrac{-1}{3}=\dfrac{5}{-15}\)
\(\dfrac{3}{-15}\)= \(\dfrac{5}{-1}\); \(\dfrac{-15}{3}=\dfrac{-1}{5}\)
b. \(\dfrac{4}{-3}=\dfrac{-12}{9};\dfrac{-3}{4}=\dfrac{9}{-12}\)
\(\dfrac{4}{-12}=\dfrac{9}{-3};\dfrac{-12}{4}=\dfrac{-3}{9}\)
c. \(\dfrac{3}{7}=\dfrac{c}{b};\dfrac{7}{3}=\dfrac{b}{c}\)
\(\dfrac{3}{c}=\dfrac{b}{7};\dfrac{c}{3}=\dfrac{7}{b}\)
d. \(\dfrac{a}{b}=\dfrac{y}{x};\dfrac{b}{a}=\dfrac{x}{y}\)
\(\dfrac{a}{y}=\dfrac{x}{b};\dfrac{y}{a}=\dfrac{b}{x}\)
chúc bạn học tốt
a) Ta có:\(\dfrac{x-3}{x+5}=\dfrac{5}{7}\)
\(\Rightarrow7\left(x-3\right)=5\left(x+5\right)\)
\(\Rightarrow7x-21=5x+25\)
\(\Rightarrow7x-5x=21+25\)
\(\Rightarrow2x=46\)
\(\Rightarrow x=46:2=23\)
\(a,\dfrac{x-3}{x+5}=\dfrac{5}{7}\\ \Leftrightarrow7x-21=5x+25\\ \Leftrightarrow2x=46\\ \Leftrightarrow x=23\)
Vậy......
\(b,\dfrac{x+4}{20}=\dfrac{5}{x+4}\\ \Leftrightarrow\left(x+4\right)^2=100\\ \Leftrightarrow x+4=\pm10\\ \Leftrightarrow x\in\left\{-14;6\right\}\)
Vậy.........
Cái này bạn áp dụng tính chất 1 của tỉ lệ thức là ra ngay mà!
Hai tỉ số bằng nhau khi tích 2 ngoại tỉ bằng tích 2 trung tỉ.
a) \(2,5:7,5=x:\dfrac{3}{5}\)
\(\Rightarrow\dfrac{2,5}{7,5}=\dfrac{x}{\dfrac{3}{5}}\)
\(\Rightarrow x=\dfrac{\dfrac{3}{5}\cdot2.5}{7,5}\)
\(\Rightarrow x=\dfrac{1}{5}\)
b) \(\dfrac{5}{6}:x=20:3\)
\(\Rightarrow\dfrac{\dfrac{5}{6}}{x}=\dfrac{20}{3}\)
\(\Rightarrow x=\dfrac{3\cdot\dfrac{5}{6}}{20}\)
\(\Rightarrow x=\dfrac{1}{8}\)
c) \(2\dfrac{2}{3}:x=1\dfrac{7}{9}\)
\(\Rightarrow\dfrac{8}{3}:x=\dfrac{16}{9}\)
\(\Rightarrow\dfrac{\dfrac{8}{3}}{x}=\dfrac{16}{9}\)
\(\Rightarrow x=\dfrac{\dfrac{8}{3}\cdot9}{16}\)
\(\Rightarrow x=\dfrac{3}{2}\)