Question

Express the following rational numbers in standard forms:

$\frac{18}{-42}$

Answer 1

A rational number is defined as a number that can be expressed in the form $\frac{\mathrm{p}}{\mathrm{q}}$ where $\mathrm{p}$ (numerator) and $\mathrm{q}$ (denominator) are integers $(\mathrm{q}\ne 0)$.

And a rational number $\frac{\mathrm{p}}{\mathrm{q}}$ is said to be in the standard form if $\mathrm{p}$ and $\mathrm{q}$ have no common factors.

So,

The HCF of $18$ and $42$ is $6$.

$\frac{18}{-42}=\frac{18÷6}{-42÷6}$ (Dividing numerator and denominator by their highest common factor $6$)

$=\frac{3}{-7}$

Hence, $-\frac{3}{7}$ is the standard form of given rational number.