To compare these numbers, we must find a common denominator.
We have dominators 4, 3 and 8.
LCM(4, 3, 8) = 24
[tex]\dfrac{1}{4}=\dfrac{1\cdot6}{4\cdot6}=\dfrac{6}{24}\\\\\dfrac{2}{3}=\dfrac{2\cdot8}{3\cdot8}=\dfrac{16}{24}\\\\\dfrac{3}{8}=\dfrac{3\cdot3}{8\cdot3}=\dfrac{9}{24}\\\\\dfrac{6}{24} < \dfrac{9}{24} < \dfrac{16}{24}\to\dfrac{1}{4} < \dfrac{3}{8} < \dfrac{2}{3}[/tex]
Answer: Dan hiked the farthest.
Other method.
[tex]\dfrac{1}{4}[/tex] is less than half, because 2 of 4 is the half
[tex]\dfrac{3}{8}[/tex] is less than half, because 4 of 8 is the half
[tex]\dfrac{2}{3}[/tex] is greater than half, because 1.5 of 3 is the half
Conclusion: [tex]\dfrac{2}{3}[/tex] is the largest fraction.
