Express the following rational number in standard form:

$\dfrac{-36}{-63}$

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 -63 is negative, so first express the rational number with a positive denominator.

$\dfrac{-36}{-63} = \dfrac{-36 \times (-1)}{-63 \times (-1)} = \dfrac{36}{63}$

The greatest common divisor of 36 and 63 is 9.

Now,

$\dfrac{36}{63} = \dfrac{36 \div 9}{63 \div 9} = \dfrac{4}{7}$

Hence, the standard form of $\mathbf{\dfrac{-36}{-63} \text{ is } \dfrac{4}{7}}$.