Question

Replace $\boxed{}$ in each of the following by the correct number:

(i) $\frac{2}{7}=\frac{6}{\boxed{}}$
(ii) $\frac{5}{8}=\frac{10}{\boxed{}}$
(iii) $\frac{4}{5}=\frac{\boxed{}}{20}$
(iv) $\frac{45}{60}=\frac{15}{\boxed{}}$
(v) $\frac{18}{24}=\frac{\boxed{}}{4}$

Answer 1

(i)
$$\begin{gathered} \frac{2}{7}=\frac{6}{} \\ \mathrm{As}2\times 3=6,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}3. \\ \Rightarrow \frac{2}{7}\times \frac{3}{3}=\frac{6}{21} \end{gathered}$$

(ii)
$$\begin{gathered} \frac{5}{8}=\frac{10}{} \\ \mathrm{As}5\times 2=10,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}2. \\ \Rightarrow \frac{5}{8}\times \frac{2}{2}=\frac{10}{16} \end{gathered}$$

(iii)
$$\begin{gathered} \frac{4}{5}=\frac{}{20} \\ \mathrm{As}5\times 4=20,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}4. \\ \Rightarrow \frac{4}{5}\times \frac{4}{4}=\frac{16}{20} \end{gathered}$$

(iv)
$$\begin{gathered} \frac{45}{60}=\frac{15}{} \\ \mathrm{As}45÷3=15,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}\hspace{0.17em}\&\mathrm{denominator}\mathrm{by}3. \\ \Rightarrow \left(\frac{{\displaystyle \frac{45}{3}}}{{\displaystyle \frac{60}{3}}}\right)=\frac{15}{20} \end{gathered}$$

(v)
$$\begin{gathered} \frac{18}{24}=\frac{}{4} \\ \mathrm{As}24÷6=4,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{by}6. \\ \Rightarrow \left(\frac{{\displaystyle \frac{18}{6}}}{{\displaystyle \frac{24}{6}}}\right)=\frac{3}{4} \end{gathered}$$