What's the difference between \( 126 \frac{1}{4} \) and \( 78 \frac{2}{3} \) ? A) \( 47 \frac{7}{12} \) B) \( 58 \frac{5}{12} \) C) \( 48 \frac{1}{3} \) D) \( 57 \frac{7}{12} \)

To find the difference between \( 126 \frac{1}{4} \) and \( 78 \frac{2}{3} \), we first convert these mixed numbers into improper fractions. 1. For \( 126 \frac{1}{4} \): \[ 126 \frac{1}{4} = \frac{126 \times 4 + 1}{4} = \frac{504 + 1}{4} = \frac{505}{4} \] 2. For \( 78 \frac{2}{3} \): \[ 78 \frac{2}{3} = \frac{78 \times 3 + 2}{3} = \frac{234 + 2}{3} = \frac{236}{3} \] Now, we need a common denominator to subtract these two fractions. The least common multiple of 4 and 3 is 12. - Convert \( \frac{505}{4} \) to twelfths: \[ \frac{505}{4} = \frac{505 \times 3}{4 \times 3} = \frac{1515}{12} \] - Convert \( \frac{236}{3} \) to twelfths: \[ \frac{236}{3} = \frac{236 \times 4}{3 \times 4} = \frac{944}{12} \] Now subtract the two fractions: \[ \frac{1515}{12} - \frac{944}{12} = \frac{1515 - 944}{12} = \frac{571}{12} \] Next, we convert \( \frac{571}{12} \) into a mixed number: - Divide 571 by 12, which gives 47 with a remainder of 7. Thus, \[ \frac{571}{12} = 47 \frac{7}{12} \] The answer is \( 47 \frac{7}{12} \), corresponding to option A.