(3) \( 2 \frac{1}{12}+4 \frac{7}{18}= \)

To add the mixed numbers \( 2 \frac{1}{12} + 4 \frac{7}{18} \), follow these steps: 1. **Separate the Whole Numbers and the Fractions:** \[ 2 \frac{1}{12} + 4 \frac{7}{18} = (2 + 4) + \left( \frac{1}{12} + \frac{7}{18} \right) = 6 + \left( \frac{1}{12} + \frac{7}{18} \right) \] 2. **Find a Common Denominator for the Fractions:** The denominators are 12 and 18. The least common multiple (LCM) of 12 and 18 is 36. 3. **Convert Each Fraction to Have the Common Denominator:** \[ \frac{1}{12} = \frac{1 \times 3}{12 \times 3} = \frac{3}{36} \] \[ \frac{7}{18} = \frac{7 \times 2}{18 \times 2} = \frac{14}{36} \] 4. **Add the Converted Fractions:** \[ \frac{3}{36} + \frac{14}{36} = \frac{17}{36} \] 5. **Combine the Whole Number with the Sum of the Fractions:** \[ 6 + \frac{17}{36} = 6 \frac{17}{36} \] 6. **Simplify if Possible:** The fraction \( \frac{17}{36} \) is already in its simplest form since 17 is a prime number and doesn't divide 36. **Final Answer:** \[ 6 \frac{17}{36} \]