Equivalent Rational Number

Equivalent rational numbers:

If the numerator and denominator of a rational number are multiplied or divided by a non-zero integer, we get a rational number which is said to be equivalent to the given rational number.

For example, consider the rational number ${\displaystyle -\frac{2}{3}}$.

${\displaystyle \frac{-2}{3}=\frac{-2\times 2}{3\times 2}=\frac{-4}{6}.}$

We see that ${\displaystyle (-\frac{2}{3}) \text{is the same as} \frac{-4}{6}.}$

${\displaystyle \frac{-2}{3}=\frac{(-2)\times (-5)}{3\times (-5)}=\frac{10}{-15}}$.

So, ${\displaystyle \frac{-2}{3} \text{is also the same as} \frac{10}{-15}.}$

Thus,

${\displaystyle \frac{-2}{3}=\frac{-4}{6}=\frac{10}{-15}}$

Such rational numbers that are equal to each other are said to be equivalent to each other.

${\displaystyle \frac{10}{-15}=\frac{10÷(-5)}{(-15)÷(-5)}=\frac{-2}{3},\frac{-12}{24}=\frac{-12÷12}{24÷12}=\frac{-1}{2}.}$