Question

Find five rational numbers equivalent to each of the following.

$\frac{5}{13}$

Answer 1

If both numerator and denominator of a rational number are either multiplied or divided by the same non zero number , we get an equivalent rational number.

$$\begin{gathered} \frac{5}{13}=\frac{5\times 2}{13\times 2}=\frac{5\times 3}{13\times 3}=\frac{5\times 4}{13\times 4}=\frac{5\times 5}{13\times 5}=\frac{5\times 6}{13\times 6} \\ \Rightarrow \frac{5}{13}=\frac{10}{26}=\frac{15}{39}=\frac{20}{52}=\frac{25}{65}=\frac{30}{78} \end{gathered}$$

So, five rational numbers equivalent to $\frac{5}{13}$ are $\frac{10}{26},\frac{15}{39},\frac{20}{52},\frac{25}{65}$ and $\frac{30}{78}.$