Question

3.cho \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\). CMR

a) \(\dfrac{a}{3b}\)= \(\dfrac{c}{3d}\)

Answer 1

đặt \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\)=k => a=bk; b=dk

\(\dfrac{a}{3b}\)=\(\dfrac{bk}{3b}=\dfrac{k}{3}\)

\(\dfrac{c}{3d}=\)\(\dfrac{dk}{3d}=\)\(\dfrac{k}{3}\)

=>\(\dfrac{a}{3b}=\)\(\dfrac{c}{3d}\)

Answer 2

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)

=> \(\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

ta có : \(\dfrac{a}{3b}=\dfrac{bk}{3b}=\dfrac{k}{3}\left(1\right)\)

lại có \(\dfrac{c}{3d}=\dfrac{dk}{3d}=\dfrac{k}{3}\left(2\right)\)

từ (1) và (2) => \(\dfrac{a}{3b}=\dfrac{c}{3d}\)