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The common denominator of the two fractions is: 24

$ \frac{13}{8 }= \frac{(3*13)}{(3*8)} =\frac{ 39}{24} $

$ \frac{7}{12 }= \frac{(2*7)}{(2*12)} =\frac{ 14}{24} $

Fractions adjusted to a common denominator

$ \frac{13}{8 }+\frac{ 7}{12 }=\frac{ 39}{24 }+\frac{ 14}{24} $

$ \frac{39}{24 }+\frac{ 14}{24 }= \frac{(14+39)}{24} $

$ \frac{(14+39)}{24 }=\frac{ 53}{24} $

$ $

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