Question

problem 1 find the sum: 2\frac{1}{6} + 2\frac{2}{5}

Explanation:

Step1: Convert to improper fractions

$2\frac{1}{6} = \frac{2\times6 +1}{6}=\frac{13}{6}$, $2\frac{2}{5}=\frac{2\times5+2}{5}=\frac{12}{5}$

Step2: Find common denominator

Common denominator of 6 and 5 is 30. Rewrite fractions:
$\frac{13}{6}=\frac{13\times5}{6\times5}=\frac{65}{30}$, $\frac{12}{5}=\frac{12\times6}{5\times6}=\frac{72}{30}$

Step3: Add the fractions

$\frac{65}{30}+\frac{72}{30}=\frac{65+72}{30}=\frac{137}{30}$

Step4: Convert back to mixed number

$\frac{137}{30}=4\frac{17}{30}$

Answer:

$4\frac{17}{30}$ (or $\frac{137}{30}$)