Question

Using the property $\frac{a}{b}=\frac{ak}{bk}$ , fill in the blanks substituting proper numbers in the following.

(i) $\frac{5}{7}=\frac{....}{28}=\frac{35}{....}=\frac{....}{3.5}$ (ii) $\frac{9}{14}=\frac{4.5}{....}=\frac{....}{42}=\frac{....}{3.5}$

Answer 1

(i)
28 = 7 × 4, 35 = 5 × 4, 3.5 = 7 × 0.5

Now,

$$\begin{gathered} \frac{5}{7}=\frac{5\times 4}{7\times 4}=\frac{5\times 7}{7\times 7}=\frac{5\times 0.5}{7\times 0.5} \\ \Rightarrow \frac{5}{7}=\frac{\underline{\mathbf{20}}}{28}=\frac{35}{\underline{\mathbf{49}}}=\frac{\underline{\mathbf{2}\mathbf{.}\mathbf{5}}}{3.5} \end{gathered}$$
(ii)
4.5 = 9 × 0.5, 42 = 14 × 3, 3.5 = 14 × 0.25

Now,

$$\begin{gathered} \frac{9}{14}=\frac{9\times 0.5}{14\times 0.5}=\frac{9\times 3}{14\times 3}=\frac{9\times 0.25}{14\times 0.25} \\ \Rightarrow \frac{9}{14}=\frac{4.5}{\underline{\mathbf{7}}}=\frac{\underline{\mathbf{27}}}{42}=\frac{\underline{\mathbf{2}\mathbf{.}\mathbf{25}}}{3.5} \end{gathered}$$