We add the two amounts of sugar: \(\displaystyle\frac{{2}}{{3}}+{1}{\left(\frac{{1}}{{4}}\right)}\)

Write the mixed fraction as an improper fraction: \(=\frac{2}{3}+\frac{5}{4}\)

Rewrite each fraction using the LCD which is 12:

\(=(\frac{2}{3})(\frac{4}{4})+(\frac{5}{4})(\frac{3}{3}) =(\frac{8}{12})+(\frac{15}{12})\)

Combine the numerators: \(=\frac{8+15}{12} =\frac{23}{12}\)

Write as a moxed fraction:

\(\displaystyle={1}{\left(\frac{{11}}{{12}}\right)}\) cups of sugar are needed.