## Thinking Mathematically (6th Edition)

$\frac{7}{12}$
Take LCM of 2 and 3 as 6. Then convert the denominator of each rational number to 6 as follows: \begin{align} & \frac{1}{2}=\frac{1\times 3}{2\times 3} \\ & =\frac{3}{6} \\ & \frac{2}{3}=\frac{2\times 2}{3\times 2} \\ & =\frac{4}{6} \end{align} Now, the rational number halfway between the provided rational numbers is: \begin{align} & \frac{\text{3}\text{.5}}{6}\text{=}\frac{35}{60} \\ & =\frac{7}{12} \end{align} Hence, the rational number halfway between the provided numbers is $\frac{7}{12}$.