The ascending arrangement of \(\dfrac{2}{3},\ \dfrac{6}{7},\ \dfrac{13}{21}\) is:
\(\dfrac{6}{7},\ \dfrac{2}{3},\ \dfrac{13}{21}\)
\(\dfrac{13}{21},\ \dfrac{2}{3},\ \dfrac{6}{7}\)
\(\dfrac{6}{7},\ \dfrac{13}{21},\ \dfrac{2}{3}\)
\(\dfrac{2}{3},\ \dfrac{6}{7},\ \dfrac{13}{21}\)
Convert to decimals: \(\dfrac{13}{21}\approx0.619,\ \dfrac{2}{3}\approx0.667,\ \dfrac{6}{7}\approx0.857\). Increasing order is \(\dfrac{13}{21},\ \dfrac{2}{3},\ \dfrac{6}{7}\).