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Ta có: \(\frac{a}{b}< \frac{c}{d}\Leftrightarrow ad< bc\)
\(\Leftrightarrow2018ad< 2018bc\)
\(\Leftrightarrow2018ad+cd< 2018bc+cd\)
\(\Leftrightarrow d\left(2018a+c\right)< c\left(2018b+d\right)\)
\(\Leftrightarrow\frac{2018a+c}{2018b+d}< \frac{c}{d}\left(đpcm\right)\)
Hình như là
a/b=2018a/2018b
Vì a/b<c/d
=>2018a/2018b<c/d
=>2018a+c/2018b+d<c+d
còn cái nịttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Vì \(\frac{a}{b}< \frac{c}{d}\Rightarrow ad< bc\)
Quy đồng mẫu hai phân số \(\frac{2019a+c}{2019b+d}\) và \(\frac{c}{d}\)
\(\frac{2019a+c}{2019b+d}=\frac{d\left(2019a+c\right)}{d\left(2019b+d\right)}=\frac{2019ad+cd}{2019bd+d^2}\)
\(\frac{c}{d}=\frac{c\left(2019b+d\right)}{d\left(2019b+d\right)}=\frac{2019bc+2019cd}{2019bd+d^2}\)
Vì ad < bc nên 2019ad + cd < 2019bc + 2019cd => \(\frac{2019a+c}{2019b+d}< \frac{c}{d}\)(đpcm)
Vì \(\frac{a}{b}< \frac{c}{d}\)
⇒ \(ad< bc\)
⇒ \(2018ad< 2018bc\)
⇒ \(2018ad+cd< 2018bc+cd\)
⇒ \(\left(2018a+c\right)d< \left(2018b+d\right)c\)
⇒ \(\frac{2018a+c}{2018b+d}< \frac{c}{d}\)
Vậy \(\frac{2018a+c}{2018b+d}< \frac{c}{d}\) (ĐPCM)
Vì \(\frac{a}{b}< \frac{c}{d}\Rightarrow\frac{a}{b}.bd< \frac{c}{d}.bd\)
\(\Rightarrow ad< bc\)
\(\Rightarrow2002ad< 2002bc\)
\(\Rightarrow2002ad+cd< 2002bc+cd\)
\(\Rightarrow\left(2002a+c\right).d< \left(2002b+d\right).c\)
Chia cả hai vế cho \(\left(2002b+d\right).d\) ta có :
\(\frac{2002a+c}{2002b+d}< \frac{c}{d}\)
Vậy...
Vì \(\frac{a}{b}< \frac{c}{d}\)
\(\Rightarrow ad< bc\)
\(\Rightarrow2002ad< 2002bc\)
\(\Rightarrow2002ad+cd< 2002bc+cd\)
\(\Rightarrow\left(2002a+c\right)d< \left(2002b+d\right)c\)
\(\Rightarrow\frac{2002a+c}{2002b+d}< \frac{c}{d}\)
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Vì a/b < c/d (Với a,b,c,d thuộc N*)
=> ad<bc
=> 2018ad < 2018bc
=> 2018ad + cd < 2018bc +cd
=> (2018a + c).d < (2018b+d).c
=> 2018a +c / 2018b + d < c/d
\(\frac{a}{b}< \frac{c}{d}\Leftrightarrow ad< bc\)
\(\Leftrightarrow2019ad< 2019bc\)
\(\Leftrightarrow2019ad+cd< 2019bc+cd\)
\(\Leftrightarrow d\left(2019a+c\right)< c\left(2019b+d\right)\)
\(\Leftrightarrow\frac{2019a+c}{2019b+d}< \frac{c}{d}\)