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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, itâ€™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:

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