Bonjour Aya299
Montrons que si a/b = c/d,
alors a/b= c/d = (ma + nc) / (mb+ nd)
En effet,
[tex]Soit\ \ \boxed{\dfrac{a}{b}=\dfrac{c}{d}=k}\\\\alors\ \ \boxed{a=bk}\ \ et\ \ \boxed{c=dk}[/tex]
Calculons [tex]\dfrac{ma+nc}{mb+nd}[/tex]
[tex]\dfrac{ma+nc}{mb+nd}=\dfrac{mbk+ndk}{mb+nd}\\\\\\\dfrac{ma+nc}{mb+nd}=\dfrac{k(mb+nd)}{mb+nd}\\\\\\\Longrightarrow\boxed{\dfrac{ma+nc}{mb+nd}=k}[/tex]
Par conséquent,
[tex]\boxed{\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{ma+nc}{mb+nd}\ (=k)}[/tex]
