Chapter 14, Problem 1RE

To determine

To simplify: The rational expression $\frac{18}{24}$.

Answer to Problem 1RE

The simplified form of the rational expression $\frac{18}{24}$ is $\underset{\_}{\frac{3}{4}}$.

Explanation of Solution

The given rational expression is $\frac{18}{24}$.

Simplify the rational expression $\frac{18}{24}$ in the factored form using prime factorization as follows.

$\begin{array}{c}\frac{18}{24}=\frac{2\left(3\right)\left(3\right)}{2\left(2\right)\left(2\right)3}\\ =\frac{\cancel{2}\left(\cancel{3}\right)\left(3\right)}{2\left(2\right)\left(\cancel{2}\right)\cancel{3}}\left(\text{Cancel the common factors}\right)\\ =\frac{3}{2\left(2\right)}\left(\text{Multiply the resultant terms}\right)\\ =\frac{3}{4}\end{array}$

Thus, the simplified form of the rational expression $\frac{18}{24}$ is $\underset{\_}{\frac{3}{4}}$.