Ta có: \(\dfrac{a}{b}\)=\(\dfrac{21}{35}\) =>\(\dfrac{a}{21}\)=\(\dfrac{b}{35}\)=k
=>a=21k ; b=35k
Ta có: ƯCLN (21k;35k)=7k=30
=>k=\(\dfrac{30}{7}\)
a=21.\(\dfrac{30}{7}\)=90
b=35.\(\dfrac{30}{7}\)=150
Vậy phân số \(\dfrac{a}{b}\)cần tìm là \(\dfrac{90}{150}\)
Giải:
Ta có: \(\frac{a}{b}=\frac{21}{35}\Rightarrow\frac{a}{b}=\frac{3}{5}\Rightarrow\frac{a}{3}=\frac{b}{5}\)
Đặt \(\frac{a}{3}=\frac{b}{5}=k\Rightarrow\left\{\begin{matrix}a=3k\\b=5k\end{matrix}\right.\)
\(UCLN\left(a;b\right)=UCLN\left(3k;5k\right)=3.5.k=15k=30\)
\(\Rightarrow k=2\)
\(\Rightarrow a=6;b=10\)
\(\Rightarrow\frac{a}{b}=\frac{6}{10}\)
Vậy \(\frac{a}{b}=\frac{6}{10}\)
