Question

6\frac{1}{6} + 5\frac{3}{10}

Explanation:

Step1: Convert to improper fractions

$6\frac{1}{6} = \frac{6\times6 + 1}{6} = \frac{37}{6}$
$5\frac{3}{10} = \frac{5\times10 + 3}{10} = \frac{53}{10}$

Step2: Find common denominator

Least common multiple of 6 and 10 is 30.
$\frac{37}{6} = \frac{37\times5}{6\times5} = \frac{185}{30}$
$\frac{53}{10} = \frac{53\times3}{10\times3} = \frac{159}{30}$

Step3: Add the fractions

$\frac{185}{30} + \frac{159}{30} = \frac{185+159}{30} = \frac{344}{30}$

Step4: Simplify and convert back

$\frac{344}{30} = \frac{172}{15} = 11\frac{7}{15}$

Answer:

$11\frac{7}{15}$ (or $\frac{172}{15}$)