Is Every Rational Number a Natural Number?
Is every rational number a natural number?
Every
natural number is a rational number but a rational number need not be a natural
number.
We know that, 1 = 1/1, 2 = 2/1, 3 = 3/1 and so on ……. .
In other words, every natural number n can be written as n = n/1, which is the quotient of two integers. Thus, every natural number is a rational number.
Clearly, 3/2, 2/5, 1/7, 15/20, etc. are rational numbers but they are not natural numbers.
Hence, every natural number is a rational number but a rational number need not be a natural number.
Let us determine whether the following rational numbers are natural numbers or not:
(i) 4/2
4/2 is a natural number. Since if we simplify 4/2 to its lowest term we get 2/1 = 2 which is a natural number.
(ii) 5/7
5/7 is not a natural number.
(iii) -15/5
-15/5 is not a natural number. Since if we simplify -15/5 to its lowest term we get -3/1 = -3 which is an integer but not a natural number.
(iv) -8/-4
-8/-4 is a natural number. Since if we simplify -8/-4 to its lowest term we get 2/1 = 2 which is a natural number.
(v) 1/10
1/10 is not a natural number.
(vi) 0/1
0/1 is not a natural number. Since 0/1 = 0 which is not a natural number.
(vii) 10/10
10/10 is a natural number. Since if we simplify 10/10 to its lowest term we get 1/1 = 1 which is a natural number.
(viii) 81/36
81/36 is not a natural number. Since, if we simplify 81/36 to its lowest term we get 9/4 which is a rational number but not a natural number.
So, from the above explanation we conclude that every rational number is not a natural number.
● 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
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