Theory:

Negative numbers are numbers that are less than zero.
For example, The negative of \(2\) is \(-2\) because \(2 + (-2) = (-2) + 2 = 0\).
 
Capture.PNG
Important!
Negative number symbol: Negative numbers are indicated by placing a dash or minus (\(-\)) sign in front, such as \(–5\), \(–12.77\). A negative number, such as \(-1\), is termed as 'negative one'.
An integer \(a\), we have, \(a + (-a) = (-a) + a = 0\); So, \(a\) is the negative of \(-a\), and \(-a\) is the negative of \(a\).
 
For example, \(2 + (-2) = (-2) + 2 = 0\), So we say \(2\) is the negative or additive inverse of \(-2\) and vice-versa.
Rational Number: A number can be made by dividing two integers. (Note: An integer is a number with no fractional part.)
For example, 1.5 is a rational number because 1.5 \(=\) 32   (3 and 2 are both integers.)
Negative numbers: A rational number is supposed to be negative if its numerator and denominator are of opposite signs such that, one of them is a positive integer, and another one is a negative integer. In additional words, a rational number is negative, if its numerator and denominator are of the opposite signs.
Example:
Each of the rational numbers  \(2/-8\), \(-30/16\), \(13/-18\), \(-15/24\) are negative rationals, but \(-11/-17\), \(2/9\), \(-3/-7\), \(1/7\) are not negative rationals.
For example, The rational number 23.
 
23 \(+\) 23 \(=\) (2+2)3 \(=\) 0.
 
Also, 23 \(+\) 23 \(=\) \(0\).
 
Similarly, 89 \(+\) 89 \(=\) 89 \(+\)89 \(=\) \(0\).
 
116 \(+\) 116 \(=\) 116 \(+\) 116 \(=\) \(0\).
 
In general, for a rational number ab, we have, ab \(+\) ab \(=\) ab \(+\) ab \(=\) \(0\).
 
We say that ab is the additive inverse of ab and ab is the additive inverse of ab.