[latex]\frac{5}{14}+\frac{1}{6}\\\\LCD(\frac{5}{14};\ \frac{1}{6})\\\\list\ the\ mulitiples\ of\ 14:\ 0;\ 14;\ 28;\ \fbox{42};\ 56;...\\\\list\ the\ multiples\ of\ 6:0;\ 6;\ 12;\ 18;\ 24;\ 30;\ 36;\ \fbox{42};\ 48;...\\\\LCD(\frac{5}{14};\ \frac{1}{6})=42\\\\\frac{5}{14}=\frac{5\times3}{14\times3}=\frac{15}{42};\ \frac{1}{6}=\frac{1\times7}{6\times7}=\frac{7}{42}\\\\Therefore:\frac{5}{14}+\frac{1}{6}=\frac{15}{42}+\frac{7}{42}=\frac{15+7}{42}=\frac{22}{42}=\boxed{\frac{11}{21}}[/latex] [latex]\frac{5}{12}-\frac{3}{8}\\\\LCD(\frac{5}{12};\ \frac{3}{8})\\\\list\ the\ multiples\ of\ 12:0;\ 12;\ \fbox{24};\ 36;...\\\\list\ the\ multiples\ of\ 8:0;\ 8;\ 16;\ \fbox{24};\ 32;...\\\\LCD(\frac{5}{12};\ \frac{3}{8})=24\\\\\frac{5}{12}=\frac{5\times2}{12\times2}=\frac{10}{24};\ \frac{3}{8}=\frac{3\times3}{8\times3}=\frac{9}{24}\\\\Therefore:\frac{5}{12}-\frac{3}{8}=\frac{10}{24}-\frac{9}{24}=\frac{10-9}{24}=\boxed{\frac{1}{24}}[/latex]

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