What is the fraction of the Earth layers, thinnest to thickest?

This depends on whether you treat the core as a single layer or split it into the outer and inner core.

The Earth's core has a radius of approximately 3,470 km whereas the Earth's crust is on average only 60 km thick.

This as a fraction is 60/3,470 which can be simplified to 1/58.

That means that the core is approximately 58 times thicker than the crust.

The mantle (which is thickest if you split the core into it's inner and outer components) is 2830 km thick.

This as a fraction is 60/2,830 which simplifies to approximately 1/47.