Express each of the following rational numbers in standard form:

Question:

Express each of the following rational numbers in standard form:

(i) $\frac{-12}{30}$

(ii) $\frac{-14}{49}$

(iii) $\frac{24}{-64}$

(iv) $\frac{-36}{-63}$

 

Solution:

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 .

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

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

$\therefore \frac{-14}{49}=\frac{-14 \div 7}{49 \div 7}=\frac{-2}{7}$ (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. 

$\therefore \frac{-24}{64}=\frac{-24 \div 8}{64 \div 8}=\frac{-3}{8}$ (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.     

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

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