1368.31 – What's That Fraction?

Twice the fraction plus half the fraction, all that times the fraction, equals the fraction. What's the fraction?

Solution

If xx is the fraction, then

(2x+x2)x=x2x+x2=1 (assuming x≠0)4x+x=25x=2x=2/5. \begin{aligned} \left( 2x + \frac{x}{2} \right) x &=& x \\ 2x + \frac{x}{2} &=& 1 \text{ (assuming } x \neq 0 \text{)} \\ 4 x + x &=& 2\\ 5x &=& 2 \\ x &=& 2/5. \end{aligned}

Two-fifths! That's the fraction. Run it through the problem's specs to make sure.