Solve Mixed Number Addition: 2 7/9 + 1 1/3 Step-by-Step

Let's solve the problem by converting the mixed numbers into improper fractions, finding a common denominator, and adding the fractions.

Step 1: Convert Mixed Numbers to Improper Fractions
- $2\frac{7}{9}$ becomes $\frac{2 \times 9 + 7}{9} = \frac{18 + 7}{9} = \frac{25}{9}$.
- $1\frac{1}{3}$ becomes $\frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3}$.

Step 2: Find a Common Denominator
- The denominators are 9 and 3. The least common denominator is 9.

Step 3: Convert Fractions to a Common Denominator
- $\frac{25}{9}$ is already with the denominator 9.
- $\frac{4}{3} = \frac{4 \times 3}{3 \times 3} = \frac{12}{9}$.

Step 4: Add the Fractions
$\frac{25}{9} + \frac{12}{9} = \frac{25 + 12}{9} = \frac{37}{9}$.

Step 5: Convert the Improper Fraction Back to a Mixed Number
- $\frac{37}{9}$ is $4 \frac{1}{9}$ because 37 divided by 9 is 4 with a remainder of 1.

Therefore, the solution to the problem $2\frac{7}{9}+1\frac{1}{3}$ is $4\frac{1}{9}$.