Answer:
[tex]\large\boxed{\dfrac{4}{5}}[/tex]
Step-by-step explanation:
Find LCD:
LCM of 15, 5 and 3 is 15
15 = (15)(1)
15 = (5)(3)
15 = (3)(5)
[tex]\dfrac{2}{5}=\dfrac{2\cdot3}{5\cdot3}=\dfrac{6}{15}\\\\\dfrac{2}{3}=\dfrac{2\cdot5}{3\cdot5}=\dfrac{10}{15}[/tex]
Therefore we have:
[tex]\dfrac{4}{15},\ \dfrac{2}{5},\ \dfrac{8}{15},\ \dfrac{2}{3}\to\dfrac{4}{15},\ \dfrac{6}{15},\ \dfrac{8}{15},\ \dfrac{10}{15}[/tex]
Look at the numerators. The next numerator is created from the previous one by adding the number 2.
Therefore the next fraction is equal to
[tex]\dfrac{10+2}{15}=\dfrac{12}{15}=\dfrac{12:3}{15:3}=\dfrac{4}{5}[/tex]
