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\frac{7}{14}+\frac{8}{14}
Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{4}{7} to fractions with denominator 14.
\frac{7+8}{14}
Since \frac{7}{14} and \frac{8}{14} have the same denominator, add them by adding their numerators.
\frac{15}{14}
Add 7 and 8 to get 15.