Solve Mixed Number Addition: 2⅗ + 4⅙ Step-by-Step

$2\frac{3}{5}+4\frac{1}{6}=$

To solve the addition of these mixed numbers, we'll follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Find a common denominator and add the fractions.
• Step 3: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step:

Step 1: Convert the mixed numbers:
For $2\frac{3}{5}$, convert to an improper fraction: $2 \times 5 + 3 = 10 + 3 = 13$, so $2\frac{3}{5} = \frac{13}{5}$.
For $4\frac{1}{6}$, convert to an improper fraction: $4 \times 6 + 1 = 24 + 1 = 25$, so $4\frac{1}{6} = \frac{25}{6}$.

Step 2: Addition of the fractions:
The denominators are 5 and 6. The least common denominator (LCD) is $30$.
Convert $\frac{13}{5}$ to $\frac{13 \times 6}{5 \times 6} = \frac{78}{30}$.
Convert $\frac{25}{6}$ to $\frac{25 \times 5}{6 \times 5} = \frac{125}{30}$.
Now add: $\frac{78}{30} + \frac{125}{30} = \frac{78 + 125}{30} = \frac{203}{30}$.

Step 3: Convert $\frac{203}{30}$ back to a mixed number:
Divide 203 by 30: The quotient is 6 and the remainder is 23.
Thus, $\frac{203}{30} = 6\frac{23}{30}$.

Therefore, the solution to the problem is $6\frac{23}{30}$, which matches choice 3.