Solve Mixed Number Addition: 6⁴/₆ + 2¹/₅

To solve $6\frac{4}{6} + 2\frac{1}{5}$, follow these steps:

• Step 1: Convert the mixed numbers to improper fractions.

$6\frac{4}{6} = \frac{6 \times 6 + 4}{6} = \frac{40}{6}$ and $2\frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}$.

• Step 2: Find a common denominator for the fractions $\frac{40}{6}$ and $\frac{11}{5}$.

The least common denominator of 6 and 5 is 30.

Convert $\frac{40}{6}$ to have the denominator 30: $\frac{40 \times 5}{6 \times 5} = \frac{200}{30}$.

Convert $\frac{11}{5}$ to have the denominator 30: $\frac{11 \times 6}{5 \times 6} = \frac{66}{30}$.

• Step 3: Add the fractions with the common denominator.

$\frac{200}{30} + \frac{66}{30} = \frac{200 + 66}{30} = \frac{266}{30}$.

• Step 4: Convert the improper fraction $\frac{266}{30}$ back to a mixed number.

Divide 266 by 30, quotient is 8 and remainder is 26: $\frac{266}{30} = 8\frac{26}{30}$.

Therefore, the solution to the problem is $8\frac{26}{30}$.