Express each of the following as a rational number in the form

Question:

Express each of the following as a rational number in the form $\frac{p}{q}$ :

(i) 6−1

(ii) (−7)−1

(iii) $\left(\frac{1}{4}\right)^{-1}$

(iv) $(-4)^{-1} \times\left(\frac{-3}{2}\right)^{-1}$

(v) $\left(\frac{3}{5}\right)^{-1} \times\left(\frac{5}{2}\right)^{-1}$

Solution:

(i) $6^{-1}=\frac{1}{6} \quad \ldots\left(a^{-1}=1 / a\right)$

(ii) $(-7)^{-1}=\frac{1}{-7} \quad \cdots\left(a^{-1}=1 / a\right)$

$=\frac{-1}{7}$

(iii) $\left(\frac{1}{4}\right)^{-1}=\frac{1}{1 / 4} \quad \cdots\left(a^{-1}=1 / a\right)$

= 4

(iv) $(-4)^{-1} \times\left(\frac{-3}{2}\right)^{-1}=\frac{1}{-4} \times \frac{1}{-3 / 2} \quad \cdots\left(a^{-1}=1 / a\right)$

$=\frac{1}{-4} \times \frac{2}{-3}$

$=\frac{1}{6}$

$(v)\left(\frac{3}{5}\right)^{-1} \times\left(\frac{5}{2}\right)^{-1}=\frac{1}{3 / 5} \times \frac{1}{5 / 2} \quad \ldots\left(a^{-1}=1 / a\right)$

$=\frac{5}{3} \times \frac{2}{5}$

$=\frac{2}{3}$

 

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