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Question

# Replace $\overline{)}$ in each of the following by the correct number: (i) $\frac{2}{7}=\frac{6}{\overline{)}}$ (ii) $\frac{5}{8}=\frac{10}{\overline{)}}$ (iii) $\frac{4}{5}=\frac{\overline{)}}{20}$ (iv) $\frac{45}{60}=\frac{15}{\overline{)}}$ (v) $\frac{18}{24}=\frac{\overline{)}}{4}$

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Solution

## (i) $\frac{2}{7}=\frac{6}{}\phantom{\rule{0ex}{0ex}}\mathrm{As}2×3=6,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}3.\phantom{\rule{0ex}{0ex}}⇒\frac{2}{7}×\frac{3}{3}=\frac{6}{21}\phantom{\rule{0ex}{0ex}}$ (ii) $\frac{5}{8}=\frac{10}{}\phantom{\rule{0ex}{0ex}}\mathrm{As}5×2=10,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}2.\phantom{\rule{0ex}{0ex}}⇒\frac{5}{8}×\frac{2}{2}=\frac{10}{16}\phantom{\rule{0ex}{0ex}}$ (iii) $\frac{4}{5}=\frac{}{20}\phantom{\rule{0ex}{0ex}}\mathrm{As}5×4=20,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}4.\phantom{\rule{0ex}{0ex}}⇒\frac{4}{5}×\frac{4}{4}=\frac{16}{20}\phantom{\rule{0ex}{0ex}}$ (iv) $\frac{45}{60}=\frac{15}{}\phantom{\rule{0ex}{0ex}}\mathrm{As}45÷3=15,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator} &\mathrm{denominator}\mathrm{by}3.\phantom{\rule{0ex}{0ex}}⇒\left(\frac{\frac{45}{3}}{\frac{60}{3}}\right)=\frac{15}{20}\phantom{\rule{0ex}{0ex}}$ (v) $\frac{18}{24}=\frac{}{4}\phantom{\rule{0ex}{0ex}}\mathrm{As}24÷6=4,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}6.\phantom{\rule{0ex}{0ex}}⇒\left(\frac{\frac{18}{6}}{\frac{24}{6}}\right)=\frac{3}{4}\phantom{\rule{0ex}{0ex}}$

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