To find the sum of [tex]\(2 \frac{2}{3} + 5 \frac{1}{3}\)[/tex], let's break down the process step by step and simplify the answer:
1. Convert the mixed numbers to improper fractions:
- For [tex]\(2 \frac{2}{3}\)[/tex]:
[tex]\[
2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}
\][/tex]
- For [tex]\(5 \frac{1}{3}\)[/tex]:
[tex]\[
5 \frac{1}{3} = 5 + \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3}
\][/tex]
2. Add the fractions:
Since both fractions have the same denominator, we can add the numerators directly:
[tex]\[
\frac{8}{3} + \frac{16}{3} = \frac{8 + 16}{3} = \frac{24}{3}
\][/tex]
3. Simplify the resulting fraction:
Divide the numerator by the denominator:
[tex]\[
\frac{24}{3} = 8
\][/tex]
Therefore, the sum of [tex]\(2 \frac{2}{3} + 5 \frac{1}{3}\)[/tex] is [tex]\(8\)[/tex].
