Question

What number must be subtracted from the numerator and added to the denominator of $\frac{13}{17}$, give a rational number equal to $\frac{1}{2}$.

Answer 1

Let $x$ be the number in the numerator,

$\frac{x}{x-\frac{13}{17}}=\frac{1}{2}$

$\Rightarrow 2x=x-\frac{13}{17}$

$\Rightarrow 2x-x=-\frac{13}{17}$

$\Rightarrow x=-\frac{13}{17}$

$\therefore$ the number is $-\frac{13}{17}$