\(\frac{1414+1515+1616+1717+1818+1919}{2020+2121+2222+2323+2424+2525}\)
\(=\frac{101\left(14+15+16+17+18+19\right)}{101\left(20+21+22+23+24+25\right)}\)
\(=\frac{\left(19+14\right)\left(19-14+1\right):2}{\left(25+20\right)\left(25-20+1\right):2}\)
=\(\frac{33.6:2}{45.6:2}=\frac{33}{45}=\frac{11}{15}\)