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a) \(\frac{3}{5}<\frac{x}{6}<\frac{4}{5}\)=> \(\frac{18}{30}<\frac{5x}{30}<\frac{24}{30}\)=> 18 < 5x < 24 => 5x = 20 => x = 20 : 5 = 4
b) \(\frac{3}{5}<\frac{2}{x}<\frac{4}{5}\)=> \(\frac{12}{20}<\frac{12}{6x}<\frac{12}{15}\)=> 20 > 6x > 15 => 6x = 18 => x = 18 : 6 = 3
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Mẫu số chung là 42 ( vì 7 x 6 = 6 x 7 = 42 )
5/7 = 5 x 6/7 x 6 = 30/42
5/6 = 5 x 7/6 x 7 = 35/42
x/y = 31/42 ; 32/42 ( 16/21 ) ; 33/42 ( 11/14 ) ; 34/42 ( 17/21 )
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\(\frac{5}{7}< \frac{x}{y}< \frac{5}{6}\)
nhân cả tử cả mẫu cả hai phân số đã biết với một số nào đó: VD số 2
\(\frac{5\times2}{7\times2}< \frac{x}{y}< \frac{5\times2}{6\times2}\)
\(\frac{10}{14}< \frac{x}{y}< \frac{10}{12}\)
\(\frac{x}{y}=\frac{10}{13}\)
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a) \(\frac{3}{5}\)< \(\frac{x}{6}\)< \(\frac{4}{5}\)
\(\frac{3\times6}{5\times6}\)< \(\frac{x\times5}{6\times5}\)< \(\frac{4\times6}{5\times6}\)
\(\frac{18}{30}\)< \(\frac{x\times5}{30}\)< \(\frac{24}{30}\)
18 < X x 5 < 24 => X x 5 = 20 => X = 4
b)\(\frac{3}{5}\)< \(\frac{2}{x}\)< \(\frac{4}{5}\)
\(\frac{3\times4}{5\times4}\)< \(\frac{2\times6}{x\times6}\)< \(\frac{4\times3}{5\times3}\)
\(\frac{12}{20}\)< \(\frac{12}{x\times6}\)< \(\frac{12}{15}\)
20 > X x 6 > 15 => X x 6 = 18 => X = 3
quy đồng mẫu số:
3/5=18/30;x/6=x×5/30;4/5=24/30
vậy x×5=19;20;21
mà x là số chia hết cho 5 nên x×5=20
x=20:5=4
ĐS:4
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3/4:2/5<X<5/4:2/5
3/4 x 5/2<X<5/4 x 5/2
15/8<X<25/8suy ra x=16;17;....;24;25
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\(\frac{5}{7}< \frac{x}{y}< \frac{5}{6}\)
\(\Rightarrow\frac{25}{35}< \frac{x}{y}< \frac{25}{30}\)
\(\Rightarrow\frac{x}{y}\in\left\{\frac{25}{31};\frac{25}{32};\frac{25}{33};\frac{25}{34}\right\}\)
Xx5=1050
X=1050:5=210
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