Question

Express the following rational numbers in standard forms:

$-\frac{32}{40}$

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 $32$ and $40$ is $8$.

$-\frac{32}{40}=-\frac{32÷8}{40÷8}$ (Dividing numerator and denominator by their highest common factor $8$)

$=-\frac{4}{5}$

Hence, $-\frac{4}{5}$ is the standard form of given rational number.