# 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 can be written as = 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

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