Solve. \( 4 \frac{6}{7}+2 \frac{1}{6}=\square \)

To solve the expression: \[ 4 \frac{6}{7} + 2 \frac{1}{6} \] Let's break it down step by step. ### Step 1: Convert Mixed Numbers to Improper Fractions 1. **Convert \(4 \frac{6}{7}\) to an improper fraction:** \[ 4 \frac{6}{7} = \frac{4 \times 7 + 6}{7} = \frac{28 + 6}{7} = \frac{34}{7} \] 2. **Convert \(2 \frac{1}{6}\) to an improper fraction:** \[ 2 \frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{12 + 1}{6} = \frac{13}{6} \] ### Step 2: Add the Improper Fractions Now, add the two improper fractions: \[ \frac{34}{7} + \frac{13}{6} \] To add these, find a common denominator. The least common multiple of 7 and 6 is 42. 1. **Convert \(\frac{34}{7}\) to have a denominator of 42:** \[ \frac{34}{7} = \frac{34 \times 6}{7 \times 6} = \frac{204}{42} \] 2. **Convert \(\frac{13}{6}\) to have a denominator of 42:** \[ \frac{13}{6} = \frac{13 \times 7}{6 \times 7} = \frac{91}{42} \] 3. **Add the two fractions:** \[ \frac{204}{42} + \frac{91}{42} = \frac{204 + 91}{42} = \frac{295}{42} \] ### Step 3: Convert Back to a Mixed Number \[ \frac{295}{42} = 7 \frac{1}{42} \] **Verification:** - \(7 \times 42 = 294\) - \(295 - 294 = 1\) So, \(\frac{295}{42} = 7 \frac{1}{42}\). ### Final Answer \[ 4 \frac{6}{7} + 2 \frac{1}{6} = 7 \frac{1}{42} \]