Simplify 2 2/4+3 2/3-1/3

To simplify the expression \( 2 \frac{2}{4} + 3 \frac{2}{3} - \frac{1}{3} \), we can first convert the mixed numbers to improper fractions and then perform the calculations.

1. Convert \( 2 \frac{2}{4} \):
\[
2 \frac{2}{4} = 2 + \frac{2}{4} = \frac{8}{4} + \frac{2}{4} = \frac{10}{4} = \frac{5}{2}
\]

2. Convert \( 3 \frac{2}{3} \):
\[
3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3}
\]

Now we can rewrite the expression using the improper fractions:

\[
\frac{5}{2} + \frac{11}{3} - \frac{1}{3}
\]

Combine the fractions \( \frac{11}{3} - \frac{1}{3} \):

\[
\frac{11}{3} - \frac{1}{3} = \frac{10}{3}
\]

Now we have:

\[
\frac{5}{2} + \frac{10}{3}
\]

Next, we need a common denominator to add these two fractions. The least common denominator between 2 and 3 is 6.

Convert \( \frac{5}{2} \) to have a denominator of 6:

\[
\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}
\]

Convert \( \frac{10}{3} \) to have a denominator of 6:

\[
\frac{10}{3} = \frac{10 \times 2}{3 \times 2} = \frac{20}{6}
\]

Now we can add them:

\[
\frac{15}{6} + \frac{20}{6} = \frac{35}{6}
\]

The final answer is:

\[
\frac{35}{6}
\]

This can also be expressed as a mixed number:

\[
5 \frac{5}{6}
\]

So, the simplified expression is \( 5 \frac{5}{6} \) or \( \frac{35}{6} \).