Question

Cho phân số a/b = 21/35 biết ƯCLN(a;b) = 30. Tìm phân số a/b.

Answer 1

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 \(\dfrac{90}{150}\)

Answer 2

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 \(\frac{a}{b}=\frac{6}{10}\)