Question

Write four equivalent rational numbers for each of the following:

$\frac{-12}{17}$

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.

$\frac{-12}{17}=\frac{-12\times 2}{17\times 2}=\frac{-24}{34}$

$\frac{-12}{17}=\frac{-12\times 3}{17\times 3}=\frac{-36}{51}$

$\frac{-12}{17}=\frac{-12\times 4}{17\times 4}=\frac{-48}{68}$

$\frac{-12}{17}=\frac{-12\times 5}{17\times 5}=\frac{-60}{85}$

Hence, $\frac{-24}{34},\frac{-36}{51},\frac{-48}{68},\frac{-60}{85}$ are the equivalent rational numbers for $\frac{-12}{17}$.