Question

A fraction equivalent to $\frac{45}{105}$ is

(a) $\frac{6}{14}$
(b) $\frac{4}{7}$
(c) $\frac{5}{7}$
(d) $\frac{7}{5}$

Answer 1

(a) $\frac{6}{14}$
$$\begin{gathered} \frac{45}{105} \\ \mathrm{On}\mathrm{dividing}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCF}\mathrm{of}45\&105,\mathrm{we}\mathrm{get}: \\ \frac{45÷15}{105÷15}=\frac{3}{7} \end{gathered}$$

$\frac{3}{7}=\frac{3}{7}\times \frac{2}{2}=\frac{6}{14}$