Is Every Rational Number a Fraction?

Is every rational number a fraction?

Every fraction is a rational number but a rational number need not be a fraction. 

Let a/b be any fraction. Then, a and b are natural numbers. Since every natural number is an integer. Therefore, a and b are integers. Thus, the fraction a/b is the quotient of two integers such that b ≠ 0. 

Hence, a/b is a rational number. 

We know that 2/-3 is a rational number but it is not a fraction because its denominator is not a natural number. 

Since every mixed fraction consisting of an integer part and a fractional part can be expressed as an improper fraction, which is quotient of two integers.

Thus, every mixed fraction is also a rational number. 

Hence, every fraction is also a rational number. 

Let us determine whether the following rational numbers are fractions or not:

(i) 1/3

1/3 is a fraction. Since both the numerator (1) and the denominator (3) are natural numbers.

(ii) 6/3

6/3 is a fraction. Since both the numerator (6) and the denominator (3) are natural numbers. 

(iii) (-5)/(-3)

(-5)/(-3) is not a fraction. Since both the numerator (-5) and the denominator (-3) are not natural numbers. 

(iv) (-17)/9           

-17/9 is not a fraction. Since the numerator is -17 and which is not a natural number. 

(v) 35/(-4)

35/(-4) is not a fraction. Since the denominator is -4 and which is not a natural number. 

(vi) 41/1

41/1 is a fraction. Since both the numerator (41) and the denominator (1) are natural numbers. 

(vii) 0/1

0/1 is not a fraction. Since the numerator is 0 and which is not a natural number. 

(viii) 1/10

1/10 is a fraction. Since both the numerator (1) and the denominator (10) are natural numbers. 

So, from the above explanation we conclude that every rational number is not a fraction.

● Rational Numbers

Introduction of 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

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

Addition of Rational Numbers

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

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers

8th Grade Math Practice

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