Sure, let's find the sum of [tex]\(8 \frac{5}{6}\)[/tex] and [tex]\(2 \frac{4}{9}\)[/tex] step by step.
1. Convert the mixed numbers to improper fractions:
For [tex]\(8 \frac{5}{6}\)[/tex]:
[tex]\[
8 \frac{5}{6} = \frac{8 \times 6 + 5}{6} = \frac{48 + 5}{6} = \frac{53}{6}
\][/tex]
For [tex]\(2 \frac{4}{9}\)[/tex]:
[tex]\[
2 \frac{4}{9} = \frac{2 \times 9 + 4}{9} = \frac{18 + 4}{9} = \frac{22}{9}
\][/tex]
2. Find a common denominator for the fractions:
The denominators are 6 and 9. The least common multiple (LCM) of 6 and 9 is 18.
3. Convert the improper fractions to have the common denominator:
For [tex]\(\frac{53}{6}\)[/tex]:
[tex]\[
\frac{53}{6} = \frac{53 \times 3}{6 \times 3} = \frac{159}{18}
\][/tex]
For [tex]\(\frac{22}{9}\)[/tex]:
[tex]\[
\frac{22}{9} = \frac{22 \times 2}{9 \times 2} = \frac{44}{18}
\][/tex]
4. Add the fractions:
[tex]\[
\frac{159}{18} + \frac{44}{18} = \frac{159 + 44}{18} = \frac{203}{18}
\][/tex]
5. Convert the resulting improper fraction back to a mixed number:
We know
[tex]\[
\frac{203}{18} \approx 11 \text{ R } 5
\][/tex]
where 11 is the quotient and 5 is the remainder, so:
[tex]\[
\frac{203}{18} = 11 \frac{5}{18}
\][/tex]
6. Check if the fractional part can be simplified:
The greatest common divisor (gcd) of 5 and 18 is 1, so the fraction [tex]\(\frac{5}{18}\)[/tex] is already in its simplest form.
Therefore, the sum of [tex]\(8 \frac{5}{6}\)[/tex] and [tex]\(2 \frac{4}{9}\)[/tex] is:
[tex]\[
11 \frac{5}{18}
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{11 \frac{5}{18}}
\][/tex]
The answer is [tex]\( \text{(c)} \)[/tex].
