Question

Write each of the following rational numbers in the standard form:
(i) $\frac{2}{10}$
(ii) $\frac{-8}{36}$
(iii) $\frac{4}{-16}$
(iv) $\frac{-15}{-35}$
(v) $\frac{299}{-161}$
(vi) $\frac{-63}{-210}$
(vii) $\frac{68}{-119}$
(viii) $\frac{-195}{275}$

Answer 1

(i) The denominator is positive and HCF of 2 and 10 is 2.

$\therefore$ Dividing the numerator and denominator by 2, we get:

$\frac{2}{10}=\frac{2/2}{10/2}=\frac{1}{5}$

(ii) The denominator is positive and HCF of 8 and 36 is 4.

$\therefore$ Dividing the numerator and denominator by 4, we get:

$\frac{-8}{36}=\frac{-8/4}{36/4}=\frac{-2}{9}$

(iii)

The denominator is negative.

$\frac{4\times -1}{-16\times -1}=\frac{-4}{16}$

HCF of 4 and 16 is 4.

$\therefore$ Dividing the numerator and denominator by 4, we get:

$\frac{-4/4}{16/4}=\frac{-1}{4}$

(iv) The denominator is negative.

$\frac{-15\times -1}{-35\times -1}=\frac{15}{35}$

HCF of 15 and 35 is 5.

$\therefore$ Dividing the numerator and denominator by 5, we get:

$\frac{15/5}{35/5}=\frac{3}{7}$

(v) The denominator is negative.

$\frac{299\times -1}{-161\times -1}=\frac{-299}{161}$

HCF of 299 and 161 is 23.

$\therefore$ Dividing the numerator and denominator by 23, we get:

$\frac{-299/23}{161/23}=\frac{-13}{7}$

(vi) The denominator is negative.

$\frac{-63\times -1}{-210\times -1}=\frac{63}{210}$

HCF of 63 and 210 is 21.

$\therefore$ Dividing the numerator and denominator by 21, we get:

$\frac{63/21}{210/21}=\frac{3}{10}$

(vii) The denominator is negative.

$\frac{68\times -1}{-119\times -1}=\frac{-68}{119}$

HCF of 68 and 119 is 17.

$\therefore$ Dividing the numerator and denominator by 17, we get:

$\frac{-68/17}{119/17}=\frac{-4}{7}$

(viii) The denominator is positive and HCF of 195 and 275 is 5.

$\therefore$ Dividing divide the numerator and denominator by 5, we get:

$\frac{-195/5}{275/5}=\frac{-39}{55}$