Question

# Find fraction equivalent of $\frac{45}{60}$, having: (i) numerator 15 (ii) denominator 4 (iii) denominator 240 (iv) numerator 135

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Solution

## (i) $\frac{45}{60}=\frac{15}{\mathrm{Denominator}}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{numerators}.\phantom{\rule{0ex}{0ex}}\mathrm{As}45÷3=15,\mathrm{we}\mathrm{will}\mathrm{divide}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}3.\phantom{\rule{0ex}{0ex}}⇒\left(\frac{\frac{45}{3}}{\frac{60}{3}}\right)=\frac{15}{20}$ (ii) $\frac{45}{60}=\frac{\mathrm{Numerator}}{4}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{denominators}.\phantom{\rule{0ex}{0ex}}\mathrm{As}60÷15=4,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}15.\phantom{\rule{0ex}{0ex}}⇒\left(\frac{\frac{45}{15}}{\frac{60}{15}}\right)=\frac{3}{4}$ (iii) $\frac{45}{60}=\frac{\mathrm{Numerator}}{240}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{denominators}.\phantom{\rule{0ex}{0ex}}\mathrm{As}60×4=240,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}4.\phantom{\rule{0ex}{0ex}}⇒\frac{45}{60}×\frac{4}{4}=\frac{180}{240}$ (iv) $\frac{45}{60}=\frac{135}{\mathrm{Denominator}}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{numerators}.\phantom{\rule{0ex}{0ex}}\mathrm{As}45×3=135,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}3.\phantom{\rule{0ex}{0ex}}⇒\frac{45}{60}×\frac{3}{3}=\frac{135}{180}$

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