Question

Write four equivalent rational numbers for each of the following:

$\frac{-2}{-9}$

Answer 1

A rational number is defined as a number that can be expressed in the form $\frac{\mathrm{p}}{\mathrm{q}}$ where $\mathrm{p}$ (numerator) and $\mathrm{q}$ (denominator) are integers $(\mathrm{q}\ne 0)$. Then $\frac{\mathrm{p}\times \mathrm{k}}{\mathrm{q}\times \mathrm{k}}$ is its equivalent rational number, where $\mathrm{k}$ is a non zero integer.

So according to the above definition lets take $\mathrm{k}=2,3,4,5,....$ and apply it in the given rational number.

$\frac{-2}{-9}=\frac{-2\times 2}{-9\times 2}=\frac{-4}{-18}=\frac{4}{18}$

$\frac{-2}{-9}=\frac{-2\times 3}{-9\times 3}=\frac{-6}{-27}=\frac{6}{27}$

$\frac{-2}{-9}=\frac{-2\times 4}{-9\times 4}=\frac{-8}{-36}=\frac{8}{36}$

$\frac{-2}{-9}=\frac{-2\times 5}{-9\times 5}=\frac{-10}{-45}=\frac{10}{45}$

Hence, $\frac{4}{18},\frac{6}{27},\frac{8}{36},\frac{10}{45}$ are the equivalent rational numbers for $\frac{-2}{-9}$.