Question

Tìm phân số \(\frac{a}{b}\)biết rằng nó bằng trung bình cộng của 3 phân số \(\frac{7}{18}\),\(\frac{11}{8}\)và \(\frac{a}{b}\)

Answer 1

Đặt \(\frac{a}{b}=k\)

Theo bài ra ta có:

\(k=\left(\frac{7}{18}+\frac{11}{8}+k\right)\div3\)

\(\Rightarrow3k=\frac{127}{72}+k\)

\(\Rightarrow2k=\frac{127}{72}\)

\(\Leftrightarrow k=\frac{127}{144}\)

Vậy, \(\frac{a}{b}=\frac{127}{144}\)

Answer 2

Ta có: \(\frac{a}{b}=\left(\frac{7}{18}+\frac{11}{8}+\frac{a}{b}\right):3\)

\(\Leftrightarrow3.\frac{a}{b}=\frac{7}{18}+\frac{11}{8}+\frac{a}{b}\)\(\Leftrightarrow3.\frac{a}{b}-\frac{a}{b}=\frac{7}{18}+\frac{11}{8}\)

\(\Leftrightarrow2.\frac{a}{b}=\frac{127}{72}\)\(\Leftrightarrow\frac{a}{b}=\frac{127}{144}\)

Vậy \(\frac{a}{b}=\frac{127}{144}\)