To solve the problem [tex]$2 \frac{5}{11} + 30 \frac{6}{11}$[/tex], let's start by breaking down the mixed numbers into their integer and fractional parts.
### Step-by-Step Solution:
1. Identify the mixed numbers:
- The first mixed number is [tex]\(2 \frac{5}{11}\)[/tex].
- The second mixed number is [tex]\(30 \frac{6}{11}\)[/tex].
2. Convert each mixed number to an improper fraction:
- For [tex]\(2 \frac{5}{11}\)[/tex]:
[tex]\[
2 \frac{5}{11} = 2 + \frac{5}{11} = \frac{2 \times 11}{11} + \frac{5}{11} = \frac{22 + 5}{11} = \frac{27}{11}
\][/tex]
- For [tex]\(30 \frac{6}{11}\)[/tex]:
[tex]\[
30 \frac{6}{11} = 30 + \frac{6}{11} = \frac{30 \times 11}{11} + \frac{6}{11} = \frac{330 + 6}{11} = \frac{336}{11}
\][/tex]
3. Add the improper fractions:
- Add the two fractions by summing their numerators (since their denominators are the same):
[tex]\[
\frac{27}{11} + \frac{336}{11} = \frac{27 + 336}{11} = \frac{363}{11}
\][/tex]
4. Convert the improper fraction back to a mixed number:
- Divide [tex]\(363\)[/tex] by [tex]\(11\)[/tex] to get the integer part and the remainder:
[tex]\[
363 \div 11 = 33 \quad \text{remainder} \, 0
\][/tex]
- This means the fraction can be written as:
[tex]\[
\frac{363}{11} = 33 \frac{0}{11}
\][/tex]
5. Combine the integer and fractional parts:
- The result in mixed number form is:
[tex]\[
33 \frac{0}{11} = 33
\][/tex]
### Final Answer:
[tex]\[
2 \frac{5}{11} + 30 \frac{6}{11} = 33
\][/tex]
