Add: \( 7 \frac{1}{4}+4 \frac{3}{7} \)

To add \( 7 \frac{1}{4} + 4 \frac{3}{7} \), start by converting the mixed numbers into improper fractions. For \( 7 \frac{1}{4} \): \[ 7 \times 4 + 1 = 28 + 1 = 29 \] So, \( 7 \frac{1}{4} = \frac{29}{4} \). For \( 4 \frac{3}{7} \): \[ 4 \times 7 + 3 = 28 + 3 = 31 \] So, \( 4 \frac{3}{7} = \frac{31}{7} \). Next, find a common denominator for \( \frac{29}{4} \) and \( \frac{31}{7} \). The least common multiple of 4 and 7 is 28. Convert both fractions: \[ \frac{29}{4} = \frac{29 \times 7}{4 \times 7} = \frac{203}{28} \] \[ \frac{31}{7} = \frac{31 \times 4}{7 \times 4} = \frac{124}{28} \] Now, add the two fractions: \[ \frac{203}{28} + \frac{124}{28} = \frac{203 + 124}{28} = \frac{327}{28} \] Convert \( \frac{327}{28} \) back to a mixed number: \( 327 \div 28 \) gives 11 remainder 19, so: \[ \frac{327}{28} = 11 \frac{19}{28} \] Thus, the final answer is: \( 7 \frac{1}{4} + 4 \frac{3}{7} = 11 \frac{19}{28} \)