Step 1 :Given the ratio of hardback books to paperback books is 6:21, we can represent the fraction of hardback books as \(\frac{6}{6+21}\)
Step 2 :Simplify the fraction: \(\frac{6}{27} = \frac{2}{9}\)
Step 3 :\(\boxed{\frac{2}{9}}\) is the fraction of hardback books on the bookshelf in its simplest form