The sum of two fractions is $14\dfrac{5}{12}$. If one of them is $7\dfrac{2}{3}$, find the other.

Given, the sum of two fractions = $14\dfrac{5}{12}$.

One of them = $7\dfrac{2}{3}$.

Other number

$\Rightarrow 14\dfrac{5}{12} - 7\dfrac{2}{3}\\[1em] \Rightarrow \dfrac{173}{12} - \dfrac{23}{3}\\[1em]$

LCM of 12 and 3 = 12.

$\Rightarrow \dfrac{173}{12} - \dfrac{23\times 4}{3\times 4}\\[1em] \Rightarrow \dfrac{173}{12} - \dfrac{92}{12}\\[1em] \Rightarrow \dfrac{173 - 92}{12}\\[1em] \Rightarrow \dfrac{81}{12}\\[1em] \Rightarrow \dfrac{27}{4}\\[1em] \Rightarrow 6\dfrac{3}{4}$

Hence, the other number = $6\dfrac{3}{4}$.