# Positive Rational Number

We will learn about the positive rational number.

A rational number is said to be positive if its numerator and denominator are either both positive integers or both negative integers.

In other words, a rational number is positive, if its numerator and denominator are of the same sign.

Each of the rational numbers 1/4, 2/9, -7/-11, -3/-13, 5/12 are positive rationals, but 2/-5, -3/10, -4/7, 11/-23 are not positive rationals.

1. Is every natural number a positive rational number?

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

In other words, any natural number n can be written as n = n/1, where n and 1 are positive integers.

Hence, every natural number is a positive (+ve) rational number.

Note: The rational number 0 is neither positive nor negative.

2. Determine whether the following rational numbers are positives or not:

(i) (-11)/3

(-11)/3 is not a positive rational. Since both the numerator and denominator are of the opposite sign.

(ii) (-5)/(-7)

(-5)/(-7) is a positive rational. Since both the numerator and denominator are negative integers.

(iii) 13/19

13/19 is a positive rational. Since both the numerator and denominator are positive integers.

(iv) 21/(-17)

21/(-17) is not a positive rational. Since both the numerator and denominator are of the opposite sign.

(v) (-105)/(-8)

(-105)/(-8) is a positive rational. Since both the numerator and denominator are negative integers.

(vi) (-3)/7

(-3)/7 is not a positive rational. Since both the numerator and denominator are of the opposite sign.

(vii) 27/31

27/31 is a positive rational. Since both the numerator and denominator are positive integers.

(viii) 25/(-27)

25/(-27) is not a positive rational. Since both the numerator and denominator are of the opposite sign.

So, from the above explanation we conclude that a rational number is positive, if its numerator and denominator are of the same sign.

Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers