30- What is the sum? \[ 2 \frac{5}{12}+3 \frac{5}{4}=\ldots \ldots \ldots \ldots \]

To find the sum of \( 2 \frac{5}{12} + 3 \frac{5}{4} \), let's break it down step by step. ### Step 1: Convert Mixed Numbers to Improper Fractions 1. **Convert \( 2 \frac{5}{12} \) to an improper fraction:** \[ 2 \frac{5}{12} = \left(2 \times 12\right) + 5 = 24 + 5 = \frac{29}{12} \] 2. **Convert \( 3 \frac{5}{4} \) to an improper fraction:** \[ 3 \frac{5}{4} = \left(3 \times 4\right) + 5 = 12 + 5 = \frac{17}{4} \] ### Step 2: Find a Common Denominator To add the fractions \(\frac{29}{12}\) and \(\frac{17}{4}\), they need a common denominator. The least common denominator (LCD) of 12 and 4 is **12**. 3. **Convert \(\frac{17}{4}\) to twelfths:** \[ \frac{17}{4} = \frac{17 \times 3}{4 \times 3} = \frac{51}{12} \] ### Step 3: Add the Fractions 4. **Add the two fractions with the common denominator:** \[ \frac{29}{12} + \frac{51}{12} = \frac{29 + 51}{12} = \frac{80}{12} \] ### Step 4: Simplify the Result 5. **Simplify \(\frac{80}{12}\):** \[ \frac{80}{12} = \frac{20}{3} = 6 \frac{2}{3} \] ### Final Answer \[ 2 \frac{5}{12} + 3 \frac{5}{4} = 6 \frac{2}{3} \]