Category: Mathematics

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.

In this article, you will learn about Positive Rational Numbers. Get to know about solved examples and explaining all about how come they are called Positive Rational Numbers. A Rational Number is said to be positive if both the numerator and denominator are either positive integers or negative integers. You can also say that a rational number is positive if both numerator and denominator are of the same sign.

1/6, 2/7, -9/-11, -5/-13, 8/12 are positive rationals, but 6/-5, -3/11, -8/7, 9/-23 are not positive rationals.

Is every natural number a positive rational number?

We know 1 = 1/1, 2 = 2/1, 3 = 3/1, 4 = 4/1 and ……..

Any natural number n can be written as n/1 where n, 1 are positive integers.

Therefore, every natural number is a positive rational number. Do remember Rational Number 0 is neither positive nor negative.

Determine whether the following rational numbers are positive or not

(i) -7/3

-7/ 3 is not a positive rational number as both the numerator and denominator are of opposite sign.

(ii) -9/-11

-9/-11 is a positive rational number as both the numerator and denominator are of the same sign.

(iii) 11/19

11/19 is a positive rational number since both numerator and denominator are positive integers.

(iv) 21/-7

21/-7 is not a positive rational number as both the numerator and denominator are of opposite sign.

(v) -105/7

-105/7 is not a positive rational number as both numerator and denominator are of opposite sign.

(vi) 25/31

25/31 is a positive rational number since both numerator and denominator are positive integers.

(vii) -6/5

-6/5 is not a positive rational number as both the numerator and denominator are of opposite sign.

(viii) 21/-25

21/-25 is not a positive rational number as both numerator and denominator are of opposite sign.

Thus, we can say that a rational number is positive if it has both numerator and denominator are of the same sign.

Every Integer is a Rational Number but a Rational Number need not be an Integer. Check out the statements, examples supporting whether or not All Rational Numbers are Integers.

We know 1 = 1/1, 2 = 2/1, 3 = 3/1 ……..

Also, -1 = -1/1, -2 = -2/1, -3 = -3/1 ……..

You can also express integer a in the form of a/1 which is also a Rational Number.

Hence, every integer is clearly a Rational Number.

Clearly, 5/2,-4/3, 3/7, etc. are all Rational Numbers but not Integers.

Therefore, every integer is a Rational Number but a Rational Number need not be an Integer. Check out the following sections and get a complete idea of the statement.

Determine whether the following Rational Numbers are Integers or not

(i) 3/5

3/5 is not an Integer and we can’t express it other than a fraction form or decimal value.

(ii) 6/3

6/3 is an integer. On simplifying 6/3 to its lowest form we get 6/3 = 2/1 which is an integer.

(iii) -3/-3

-3/-3 is an integer. On reducing -3/-3 to its reduced form we get -1/-1 =1 which is an integer.

(iv) -13/2

-13/2 is not an integer and we can’t express it other than a fraction form or decimal value.

(v) -36/9

-36/9 is an integer as we get the reduced form -36/9=-4 which is an integer.

(vi) 47/-9

47/-9 is not an integer and we can’t express it other than fraction form or decimal value.

(vii) -70/-20

-70/-20 is not an integer and we can’t express it other than fraction form or decimal value.

(viii) 1000/-10

1000/-10 is an integer as we get 1000/-10 = -100 on reducing to its lowest form and -100 is an integer.

From the above instances, we can conclude that Not Every Rational Number is an Integer.

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Know whether zero falls under Rational Numbers or not and the statements supporting it here. Yes, Zero is a Rational Number and you will have clarity on it by the end. As we can write the Integer 0 in any of the below forms.

For instance, 0/1, 0/-1, 0/2, 0/-2, 0/3, 0/-3, 0/4, 0/-4 …..

In other words, we can express as 0 = 0/b where b is a non zero integer.

Thus, you can write 0 as a/b = 0 where a is 0 and the denominator b is a non- zero integer.

Therefore, 0 is a Rational Number.

Examples

(i) 0/6

0/6 is a rational number as we have the denominator non- zero integer.

(ii) 0/-2

0/-2 is a rational number since -2 is an integer and is non zero.

(iii) 0/10

0/10 is a rational number since we have 12 in the denominator which is a non zero integer.

Thus, the above instances prove that 0 is a Rational Number.