fine, thin
tattered
the tattered shreds of their flag

in shreds, into shreds
Cut the orange peel into thin shreds.
Their economy is in shreds. (figurative)

shred of
Just a few shreds of cloth were left.

cut, rip, tear, etc. sth to shreds (figurative)
Their case was torn to shreds by the lawyer.

every
With her had gone every shred of hope he had for the future.

last, remaining
She was hanging on to the last remaining shreds of her reputation.

one, single, slightest (all used in negative phrases)
There is not one shred of evidence in this case.

shred of
There is not a shred of doubt in my mind that we will win.

without a shred of sth
This is an old story without a shred of truth to it.