Calculate the Sum: 6¼ + 1⅔ + 2⅚ Mixed Number Addition

To solve this problem, we'll convert each mixed number to an improper fraction and then find a common denominator for the addition:

• Convert each mixed number to an improper fraction:
• $6\frac{2}{4} = \frac{6 \times 4 + 2}{4} = \frac{26}{4}$
• $1\frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{10}{6}$
• $2\frac{7}{12} = \frac{2 \times 12 + 7}{12} = \frac{31}{12}$
• Find the least common denominator (LCD) of 4, 6, and 12, which is 12.
• Rewrite each fraction with the common denominator:
• $\frac{26}{4} = \frac{26 \times 3}{4 \times 3} = \frac{78}{12}$
• $\frac{10}{6} = \frac{10 \times 2}{6 \times 2} = \frac{20}{12}$
• $\frac{31}{12}$ is already over 12.
• Add the fractions:
• $\frac{78}{12} + \frac{20}{12} + \frac{31}{12} = \frac{78 + 20 + 31}{12} = \frac{129}{12}$
• Convert $\frac{129}{12}$ to a mixed number:
• Divide 129 by 12. This yields 10 with a remainder of 9.
• Therefore, the mixed number form is $10\frac{9}{12}$.
• Simplify $\frac{9}{12}$ to $\frac{3}{4}$.

Thus, the final result of the addition is $10\frac{3}{4}$.

The correct answer matches choice 4: $10\frac{3}{4}$.