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.
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Thus, every mixed fraction is also a rational number.
Hence, every fraction is also a rational number.
Let us determinewhether the following rational numbers are fractions or not:
(i) 1/3
1/3 is a fraction. Since both the numerator (1) and thedenominator (3) are natural numbers.
(ii) 6/3
6/3 is a fraction. Since both the numerator (6) and thedenominator (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 whichis not a natural number.
(v) 35/(-4)
35/(-4) is not a fraction. Since the denominator is -4 andwhich is not a natural number.
(vi) 41/1
41/1 is a fraction. Since both the numerator (41) and thedenominator (1) are natural numbers.
(vii) 0/1
0/1 is not a fraction. Since the numerator is 0 and which isnot a natural number.
(viii) 1/10
1/10 is a fraction. Since both the numerator (1) and thedenominator (10) are natural numbers.
So, from the above explanation we conclude that everyrational number is not a fraction.
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● 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 Numberson 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
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