Question

Find five rational numbers equivalent to each of the following.

$\frac{2}{-7}$

Answer 1

Finding the equivalent rational number

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.

$$\begin{gathered} \Rightarrow \frac{2}{-7}=\frac{2\times 2}{-7\times 2}=\frac{4}{-14} \\ \Rightarrow \frac{2}{-7}=\frac{2\times 3}{-7\times 3}=\frac{6}{-21} \\ \Rightarrow \frac{2}{-7}=\frac{2\times 4}{-7\times 4}=\frac{8}{-28} \\ \Rightarrow \frac{2}{-7}=\frac{2\times 5}{-7\times 5}=\frac{10}{-35} \\ \Rightarrow \frac{2}{-7}=\frac{2\times 6}{-7\times 6}=\frac{12}{-42} \end{gathered}$$

So, five rational numbers equivalent to $\frac{2}{-7}$ are $\frac{4}{-14},\frac{6}{-21},\frac{8}{-28},\frac{10}{-35}$ and $\frac{12}{-42}.$