Question

Find five rational numbers equivalent to the following.

$\frac{-1}{9}$

Answer 1

Finding five equivalent rational numbers.

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.

$$\begin{gathered} \frac{-1}{9}=\frac{-1\times 2}{9\times 2}=\frac{-1\times 3}{9\times 3}=\frac{-1\times 4}{9\times 4}=\frac{-1\times 5}{9\times 5}=\frac{-1\times 6}{9\times 6} \\ \Rightarrow \frac{-1}{9}=\frac{-2}{18}=\frac{-3}{27}=\frac{-4}{36}=\frac{-5}{45}=\frac{-6}{54} \end{gathered}$$

Hence, five rational numbers equivalent to $\frac{-1}{9}$ are $\frac{-2}{18},\frac{-3}{27},\frac{-4}{36},\frac{-5}{45}$ and $\frac{-6}{54}.$