To divide by a common fraction, multiply by the reciprocal:
8 ÷ 1/3 = 8 x 3/1 = 8 x 3 = ...
8 divided by one thrid: $${\frac{{\mathtt{8}}}{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}} = {\mathtt{24}}$$
8 divided by 3: $${\frac{{\mathtt{8}}}{{\mathtt{3}}}} = {\mathtt{2.666\: \!666\: \!666\: \!666\: \!666\: \!7}}$$
8 divided by 1/3 of 8: $${\frac{{\mathtt{8}}}{\left({\frac{{\mathtt{8}}}{{\mathtt{3}}}}\right)}} = {\mathtt{3}}$$