problem: If $A=\frac{1}{4}$ and $B=-\frac{1}{2}$, what is the absolute value of the difference between $18A$ and $18B$? Express your answer as a decimal to the nearest tenth.
solution: We are looking for $|18A-18B|$, which we can rewrite as $|18(A-B)|=18|A-B|$.  Since $A-B=\frac{1}{4}-\left(-\frac{1}{2}\right)=\frac{3}{4}$, we find $18|A-B|=18\cdot\frac{3}{4}=\frac{27}{2}=\boxed{13.5}$.