[tex]\text{The sum of two rational numbers is}\ 5\dfrac{1}{2}.\\\\\text{One of the numbers is}\ 6\dfrac{3}{14}.\\\\5\dfrac{1}{2}+x=6\dfrac{3}{14}\Rightarrow x=5\dfrac{1}{2}-6\dfrac{3}{14}\\\\\text{We must find the common denominator. It's 14.}\\\\14=2\cdot7\to5\dfrac{1}{2}=5\dfrac{1\cdot7}{2\cdot7}=5\dfrac{7}{14}\\\\5\dfrac{7}{14}-6\dfrac{3}{14}=-\left(6\dfrac{3}{14}-5\dfrac{7}{14}\right)=-\left(5\dfrac{14+3}{14}-5\dfrac{7}{14}\right)[/tex]
[tex]=-\left(5\dfrac{17}{14}-5\dfrac{7}{14}\right)=-\dfrac{10}{14}=-\dfrac{10:2}{14:2}=-\dfrac{5}{7}\\\\Answer:\ -\dfrac{5}{7}\\\\Check:\\\\6\dfrac{3}{14}+\left(-\dfrac{5}{7}\right)=6\dfrac{3}{14}-\dfrac{5}{7}=6\dfrac{3}{14}-\dfrac{5\cdot2}{7\cdot2}=6\dfrac{3}{14}-\dfrac{10}{14}\\\\=5\dfrac{14+3}{14}-\dfrac{10}{14}=5\dfrac{17}{14}-\dfrac{10}{14}=5\dfrac{7}{14}=5\dfrac{7:7}{14:7}=5\dfrac{1}{2}\ \ \ CORRECT[/tex]
