Express the following rational number in standard form:

$\dfrac{24}{-64}$

A rational number $\dfrac{p}{q}$ is in standard form if $q \gt 0$ and $p, q$ have no common divisor other than 1.

Here the denominator -64 is negative, so first express the rational number with a positive denominator.

$\dfrac{24}{-64} = \dfrac{24 \times (-1)}{-64 \times (-1)} = \dfrac{-24}{64}$

The greatest common divisor of 24 and 64 is 8.

Now,

$\dfrac{-24}{64} = \dfrac{-24 \div 8}{64 \div 8} = \dfrac{-3}{8}$

Hence, the standard form of $\mathbf{\dfrac{24}{-64} \text{ is } \dfrac{-3}{8}}$.