\(\left(\dfrac{101}{303}+\dfrac{2022}{5055}+\dfrac{4004}{15015}\right)\times2022=\left(\dfrac{1}{3}+\dfrac{2}{5}+\dfrac{4}{15}\right)\times2022=\left(\dfrac{5}{15}+\dfrac{6}{15}+\dfrac{4}{15}\right)\times2022=\left(\dfrac{5+6+4}{15}\right)\times2022=\dfrac{15}{15}\times2022=1\times2022=2022\)