If A = 0.142857142857 _____ and B = 0.16666 _____, then what is the value of (A + B)/AB?
13
The repeating decimals are standard: \(A=0.\overline{142857}=\dfrac{1}{7}\) and \(B=0.1\overline{6}=\dfrac{1}{6}\).
Use the algebraic shortcut:
\[\frac{A+B}{AB}=\frac{1}{A}+\frac{1}{B}=7+6=13\]
Therefore the value is 13.
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