Puzzle of the Week #203 - Fractions

1/3 = 0.333… and 3/8 = 0.375. No fraction with a single-digit denominator lies between them.

What is the fraction greater than 1/3 and less than 3/8 that has the lowest denominator? Call that fraction ‘x’.

What is the fraction greater than ‘x’ and less than 3/8 that has the lowest denominator? Call that fraction ‘y’.

Finally, what is the fraction greater than ‘x’ and less than ‘y’ that has the lowest denominator?