Question

Question 86 (i)

Find the reciprocal of the following:
$(\frac{1}{2}\times \frac{1}{4})+(\frac{1}{2}\times 6)$

Answer 1

Reciprocal of any rational number of the form $\frac{p}{q}$ is equal to $\frac{q}{p}.$

Given $(\frac{1}{2}\times \frac{1}{4})+(\frac{1}{2}\times 6)=\frac{1\times 1}{2\times 4}+\frac{1\times 6}{2\times 1}=\frac{1}{8}+\frac{6}{2}=\frac{1\times 1}{8\times 1}+\frac{6\times 4}{2\times 4}=\frac{1}{8}+\frac{24}{8}=\frac{1+24}{8}=\frac{25}{8}$
Hence, the reciprocal of $\frac{25}{8}$ is $\frac{8}{25}.$