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Can Rational Numbers be Negative?

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Rational numbers are those numbers which can be expressed in fraction i.e. a number having both numerator and denominator. Both numerator and denominator both are integers. The query comes in our mind is that can rational numbers be negative or  not. Now, it’s clear that every number is a rational number, because every number has 1 as its denominator. For example, 23 can be written as $\frac{23}{1}$. Thus, 23 is a rational number.

Some more examples of rational numbers are as follows:

  1. $\frac{2}{3}$
  2. $\frac{15}{19}$
  3. $\frac{457845}{96587}$
  4. $\frac{652}{84}$
  5. $\frac{47}{7}$
Now, we will see whether a rational number can be negative.

A negative sign do not have any relevance with the property of being rational number and do not affect the final outcome in value. Therefore, a rational number can be negative.

Let us see some examples of negative rational numbers: 
  1. $\frac{-5}{6}$
  2. $\frac{-71}{2564}$
  3. $\frac{-53}{75}$ 
  4. $\frac{-8}{9}$
  5. $\frac{-21}{10}$
Let us see some examples:
 

Example 1: 

Find the positive and negative rational numbers in the following list.

1, $\frac{-2}{3}$, $\frac{8}{9}$, $\frac{18}{19}$, $\frac{-7}{3}$, $\frac{-7}{8}$, 45, $\frac{-16}{13}$, $\frac{45}{96}$, $\frac{-78}{93}$.

Solution:

Positive rational numbers as follows:

1, $\frac{8}{9}$, $\frac{18}{19}$, 45, $\frac{45}{96}$

Negative rational numbers are as follows:

$\frac{-2}{3}$, $\frac{-7}{3}$, $\frac{-7}{8}$, $\frac{-16}{13}$, $\frac{-78}{93}$.
 

Example 2: 

Find the positive and negative rational numbers in the following list.

21, $\frac{-12}{31}$, $\frac{58}{9}$, $\frac{181}{194}$, $\frac{-17}{37}$, $\frac{-17}{8}$, 445, $\frac{-168}{113}$, $\frac{145}{96}$, $\frac{-278}{93}$, $\frac{-96}{78}$, $\frac{72}{45}$

Solution:

Positive rational numbers are as follows:

21, $\frac{58}{9}$, $\frac{181}{194}$, 445, $\frac{145}{96}$, $\frac{72}{45}$

Negative rational number are as follows:

$\frac{-12}{31}$, $\frac{-17}{37}$, $\frac{-17}{8}$, $\frac{-168}{113}$, $\frac{-278}{93}$, $\frac{-96}{78}$.