Question

If $\frac{a}{b}=\frac{5}{8}$, find the values of the following ratios:

(i) b : a

(ii) $\frac{a+b}{b}$

(iii) $\frac{a-b}{b}$

(iv) $\frac{a+b}{a-b}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\frac{a}{b}=\frac{5}{8} \\ \therefore \frac{b}{a}=\frac{8}{5}\left(\mathrm{Invertendo}\right) \\ \left(\mathrm{ii}\right)\frac{a}{b}=\frac{5}{8} \\ \therefore \frac{a+b}{b}=\frac{5+8}{8}\left(\mathrm{Componendo}\right) \\ =\frac{a+b}{b}=\frac{13}{8} \\ \left(\mathrm{iii}\right)\frac{a}{b}=\frac{5}{8} \\ \therefore \frac{a-b}{b}=\frac{5-8}{8}\left(\mathrm{Dividendo}\right) \\ =\frac{a-b}{b}=\frac{-3}{8} \\ \left(\mathrm{iv}\right)\frac{a}{b}=\frac{5}{8} \\ \therefore \frac{a+b}{a-b}=\frac{5+8}{5-8}(\mathrm{Componendo}\&\mathrm{dividendo}) \\ =\frac{a+b}{a-b}=\frac{13}{-3} \end{gathered}$$