Solve Mixed Number Addition: 4 2/3 + 1 1/4

To solve this problem, we'll add two mixed numbers, $4\frac{2}{3}$ and $1\frac{1}{4}$, by following these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Find a common denominator and adjust fractions accordingly.
• Step 3: Add the fractions and simplify.
• Step 4: Convert the result back to a mixed number, if necessary.

Let's carry out each step in detail:

Step 1: Convert to Improper Fractions
For $4\frac{2}{3}$, convert to: $\frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}$.
For $1\frac{1}{4}$, convert to: $\frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4}$.

Step 2: Find the Common Denominator
The denominators are 3 and 4. The least common multiple (LCM) is 12.

Convert $\frac{14}{3}$ to a denominator of 12: $\frac{14 \times 4}{3 \times 4} = \frac{56}{12}$.
Convert $\frac{5}{4}$ to a denominator of 12: $\frac{5 \times 3}{4 \times 3} = \frac{15}{12}$.

Step 3: Add the Fractions
Add $\frac{56}{12}$ and $\frac{15}{12}$:
$\frac{56}{12} + \frac{15}{12} = \frac{56 + 15}{12} = \frac{71}{12}$.

Step 4: Convert to a Mixed Number
Divide 71 by 12. The quotient is 5 and the remainder is 11, so:
$\frac{71}{12} = 5\frac{11}{12}$.

Therefore, the solution to the problem is $5\frac{11}{12}$.