Add. Then write the sum in lowest terms. \[ \begin{array}{r} 7 \frac{5}{12} \\ +4 \frac{11}{12} \\ \hline \end{array} \]

Step 1 ：Given the mixed numbers \(7 \frac{5}{12}\) and \(4 \frac{11}{12}\)

Step 2 ：To add these mixed numbers, we can add the whole numbers together and the fractions together separately.

Step 3 ：Adding the whole numbers, we get \(7 + 4 = 11\)

Step 4 ：Adding the fractions, we get \(\frac{5}{12} + \frac{11}{12} = \frac{16}{12}\)

Step 5 ：\(\frac{16}{12}\) is an improper fraction, so we convert it to a mixed number. This gives us \(1 \frac{4}{12}\)

Step 6 ：We simplify \(\frac{4}{12}\) to \(\frac{1}{3}\)

Step 7 ：Adding the whole number part of the fraction to the sum of the whole numbers, we get \(11 + 1 = 12\)

Step 8 ：So, the sum of the two mixed numbers is \(12 \frac{1}{3}\)

Step 9 ：Final Answer: \(\boxed{12 \frac{1}{3}}\)