Express $\dfrac{-6}{11}$ as a rational number with numerator

(i) -36

(ii) 42

(i) Numerator -36

Clearly, (-6) x 6 = -36.

So, we multiply the numerator as well as the denominator of the given rational number by 6.

$\dfrac{-6}{11} = \dfrac{(-6) \times 6}{11 \times 6} = \dfrac{-36}{66}$

∴ The rational number with numerator $-36$ is $\dfrac{-36}{66}$.

(ii) Numerator 42

Clearly, (-6) x (-7) = 42.

So, we multiply the numerator as well as the denominator of the given rational number by -7.

$\dfrac{-6}{11} = \dfrac{(-6) \times (-7)}{11 \times (-7)} = \dfrac{42}{-77}$

∴ The rational number with numerator $42$ is $\dfrac{42}{-77}$.