Question

Find fraction equivalent of $\frac{45}{60}$, having:

(i) numerator 15
(ii) denominator 4
(iii) denominator 240
(iv) numerator 135

Answer 1

(i)
$$\begin{gathered} \frac{45}{60}=\frac{15}{\mathrm{Denominator}} \\ \mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{numerators}. \\ \mathrm{As}45÷3=15,\mathrm{we}\mathrm{will}\mathrm{divide}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}3. \\ \Rightarrow \left(\frac{{\displaystyle \frac{45}{3}}}{{\displaystyle \frac{60}{3}}}\right)=\frac{15}{20} \end{gathered}$$

(ii)
$$\begin{gathered} \frac{45}{60}=\frac{\mathrm{Numerator}}{4} \\ \mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{denominators}. \\ \mathrm{As}60÷15=4,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}15. \\ \Rightarrow \left(\frac{{\displaystyle \frac{45}{15}}}{{\displaystyle \frac{60}{15}}}\right)=\frac{3}{4} \end{gathered}$$

(iii)
$$\begin{gathered} \frac{45}{60}=\frac{\mathrm{Numerator}}{240} \\ \mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{denominators}. \\ \mathrm{As}60\times 4=240,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}4. \\ \Rightarrow \frac{45}{60}\times \frac{4}{4}=\frac{180}{240} \end{gathered}$$

(iv)
$$\begin{gathered} \frac{45}{60}=\frac{135}{\mathrm{Denominator}} \\ \mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{numerators}. \\ \mathrm{As}45\times 3=135,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}3. \\ \Rightarrow \frac{45}{60}\times \frac{3}{3}=\frac{135}{180} \end{gathered}$$