Question

Express each of the following rational numbers in standard form:
(i) $\frac{-12}{30}$
(ii) $\frac{-14}{49}$
(iii) $\frac{24}{-64}$
(iv) $\frac{-36}{-63}$

Answer 1

A rational number $\frac{a}{b}$ is said to be in the standard form if $a$ and $b$ have no common divisor other than unity and $b>0$.
Thus,

(i) The greatest common divisor of 12 and 30 is 6.

∴ $\frac{-12}{30}=\frac{-12÷6}{30÷6}=\frac{-2}{5}$ (In the standard form)

(ii)The greatest common divisor of 14 and 49 is 7.

∴ $\frac{-14}{49}=\frac{-14÷7}{49÷7}=\frac{-2}{7}$ (In the standard form)

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

The greatest common divisor of 24 and 64 is 8.

∴ $\frac{-24}{64}=\frac{-24÷8}{64÷8}=\frac{-3}{8}$ (In the standard form)

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

The greatest common divisor of 36 and 63 is 9.

∴ $\frac{36}{63}=\frac{36÷9}{63÷9}=\frac{4}{7}$ (In the standard form)