6.) \( 2 \frac{2}{3}+1 \frac{4}{9}=2-1 \frac{4}{9}= \)

Let's break down the addition of the mixed numbers first. To add \(2 \frac{2}{3}\) and \(1 \frac{4}{9}\), we convert them into improper fractions. \(2 \frac{2}{3}\) becomes \(\frac{8}{3}\) and \(1 \frac{4}{9}\) becomes \(\frac{13}{9}\). Finding a common denominator (which is 9), we convert \(\frac{8}{3}\) to \(\frac{24}{9}\). Now we add: \(\frac{24}{9} + \frac{13}{9} = \frac{37}{9}\) or \(4 \frac{1}{9}\). Next, for \(2 - 1 \frac{4}{9}\), we first convert \(1 \frac{4}{9}\) into an improper fraction, which gives us \(\frac{13}{9}\). Then, we rewrite 2 as \(\frac{18}{9}\) and perform the subtraction: \(\frac{18}{9} - \frac{13}{9} = \frac{5}{9}\). So, the final result is: \(2 \frac{2}{3} + 1 \frac{4}{9} = 4 \frac{1}{9}\) and \(2 - 1 \frac{4}{9} = \frac{5}{9}\).