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
Introduction of Rational Numbers
Is Every Rational Number a Natural Number?
Is Every Rational Number an Integer?
Is Every Rational Number a Fraction?
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
Rational Numbers in Descending Order
Representation of Rational Numbers on the Number Line
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 Same Denominator
Subtraction of Rational Number with Different Denominator
Subtraction of Rational Numbers
Properties of Subtraction of Rational Numbers
Rational Expressions Involving Addition and Subtraction
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
Reciprocal of a Rational Number
Rational Expressions Involving Division
Properties of Division of Rational Numbers
Rational Numbers between Two Rational Numbers
8th Grade Math Practice
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● Rational Numbers  Worksheets
Worksheet on Equivalent Rational Numbers
Worksheet on Lowest form of a Rational Number
Worksheet on Standard form of a Rational Number
Worksheet on Equality of Rational Numbers
Worksheet on Comparison of Rational Numbers
Worksheet on Representation of Rational Number on a Number Line
Worksheet on Adding Rational Numbers
Worksheet on Properties of Addition of Rational Numbers
Worksheet on Subtracting Rational Numbers
Worksheet on Addition and
Subtraction of Rational Number
Worksheet on Rational Expressions Involving Sum and Difference
Worksheet on Multiplication of Rational Number
Worksheet on Properties of Multiplication of Rational Numbers
Worksheet on Division of Rational Numbers
Worksheet on Properties of Division of Rational Numbers
Worksheet on Finding Rational Numbers between Two Rational Numbers
Worksheet on Word Problems on Rational Numbers