### Theory:

Equivalent fractions:

Fractions like $\frac{1}{2},\frac{2}{4},\frac{3}{6},\frac{4}{8}$ have a different numerator and different denominator but represent the same value. These are called equivalent fractions. To find the equivalent fraction of a given fraction, multiply numerator and denominator by the same number.
Example:
$$1/5$$ can be converted into its equivalent fraction as, $\frac{1×2}{5×2}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{2}{10};\phantom{\rule{0.147em}{0ex}}\frac{1×3}{5×3}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{3}{15\phantom{\rule{0.147em}{0ex}}}\phantom{\rule{0.147em}{0ex}}$.
The standard form of rational numbers:

A rational number $\frac{p}{q}$ is in standard form if its denominator is positive and the common factor between numerator and denominator should be $$1$$.

Steps to convert rational numbers into the standard form:

1. A rational number in the standard form, it will not have a negative sign in the denominator, so $\frac{p}{-q}$ should be taken as $\frac{-p}{q}$.

2. Divide the numerator $$p$$ and denominator $$q$$ by their HCF (Highest Common Factor).
Example:
Write $\frac{12}{-8}$ in standard form.
1. Take the negative sign from denominator to the numerator, $\frac{-12}{8}$.

2.HCF (Highest Common Factor) of numerator $$12$$ and denominator $$8$$ is $$4$$. Divide numerator $$12$$ and denominator $$8$$ by $$4$$ which is equal to $\frac{-3}{2}$ that is $\frac{-12÷4}{8÷4}=\frac{-3}{2}$.

Thus, the standard form of $\frac{-12}{8}$ is $\frac{-3}{2}$.