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.
I need to find the absolute value of the difference between $18A$ and $18B$. First, I'll simplify $18A$ and $18B$ by multiplying $18$ by $\frac{1}{4}$ and $-\frac{1}{2}$. I get $18A=18\cdot\frac{1}{4}=\frac{18}{4}=\frac{9}{2}$ and $18B=18\cdot-\frac{1}{2}=-\frac{18}{2}=-9$. Next, I'll subtract $18B$ from $18A$ to get the difference. I get $18A-18B=\frac{9}{2}-(-9)=\frac{9}{2}+9=\frac{9+18}{2}=\frac{27}{2}$. Finally, I'll take the absolute value of this difference and express it as a decimal. I get $|\frac{27}{2}|=\frac{27}{2}=13.5$. 