Question

8\frac{5}{6} + 2\frac{2}{3}

Explanation:

Step1: Convert mixed numbers to improper fractions or adjust fractions to have a common denominator. Let's adjust the second fraction to have denominator 6.

$2\frac{2}{3} = 2\frac{4}{6}$ (since $\frac{2}{3}=\frac{2\times2}{3\times2}=\frac{4}{6}$)

Step2: Add the whole numbers and the fractions separately.

Whole numbers: $8 + 2 = 10$
Fractions: $\frac{5}{6}+\frac{4}{6}=\frac{5 + 4}{6}=\frac{9}{6}=\frac{3}{2}=1\frac{1}{2}$

Step3: Add the results from step 2.

$10+1\frac{1}{2}=11\frac{1}{2}$ (or as an improper fraction, $\frac{23}{2}$)
Alternatively, convert both to improper fractions:
$8\frac{5}{6}=\frac{8\times6 + 5}{6}=\frac{53}{6}$
$2\frac{2}{3}=\frac{2\times3+2}{3}=\frac{8}{3}=\frac{16}{6}$
Then add: $\frac{53}{6}+\frac{16}{6}=\frac{53 + 16}{6}=\frac{69}{6}=\frac{23}{2}=11\frac{1}{2}$

Answer:

$11\frac{1}{2}$ (or $\frac{23}{2}$)