Get a Complete Idea of Negative Rational Numbers from this article. You can see the conditions for Negative Rational Numbers along with a few examples.
A Rational Number is said to be negative if the numerator and denominator are of opposite sign i.e. any one of them is a positive integer and the other is a negative integer. You can also say that a Rational Number is Negative if the numerator and denominator are of opposite signs.
All the Rational Numbers -1/7, 4/-5, -25/11, 10/-19, -13/23 are negative. Rational Numbers -11/-14, 2/3, -3/-4, 1/2 are not negative.
Is every negative integer a negative rational number?
We know -1 = -1/1, -2 = -2/1, -3 = -3/1, -4 = -4/1 ……
We can express negative integer n in the form of n/1 where n is a negative integer and 1 is a positive integer.
Thus, every negative integer is a negative rational number. On the other hand, Rational Number 0 is neither positive nor negative.
Determine whether the following rational numbers are negative or not?
(i) 3/(-6)
3/(-6) is a negative rational since the denominator and numerator are having opposite signs.
(ii) (-1)/(-4)
(-1)/(-4) is not a negative rational as both the numerator and denominator are having the same sign.
(iii) 11/23
11/23 is not a negative rational since both the numerator and denominator are of the same sign.
(iv) 9/-14
9/-14 is a negative rational since both the numerator and denominator are of opposite signs.
(v) (-64)/(-8)
(-64)/(-8) is not a negative rational as both the numerator and denominator are of the same sign.
(vi) 20/24
20/24 is not a negative rational as you have both the numerator and denominator of the same sign.
(vii) (-13)/39
(-13)/39 is a negative rational since we have both the numerator and denominator of opposite signs.
(viii) (-31)/7
(-31)/7 is a negative rational since we have both the numerator and denominator of opposite signs.
Thus, from the above examples, we can say that a negative rational number is the one that has both the numerator and the denominator of the opposite sign.