# Properties Of Rational Number

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```					             Properties Of Rational Number
Properties Of Rational Number

We will discuss different properties of rational numbers in this session. Rational numbers are
the numbers which can be expressed in the form of p/q, where p and q are the integers and q
in not equal to zero. Here we will take the properties of rational numbers:

1. Closure property: We mean by closure property that if there are two rational numbers, then

Closure property of addition holds true, which means that the sum of two rational numbers is
also a rational number.

Closure property of subtraction holds true, which means that if there exist two rational
numbers, then the difference of the two rational numbers is also a rational number.

Closure property of multiplication holds true, which means that if there exist two rational
numbers, then the product of the two rational numbers is also a rational number.

Closure property of division holds true, which means that if there exist two rational numbers,
then the quotient of the two rational numbers is also a rational number.

Know More About Fourier Transform Of Coulomb Potential

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2. Commutative property of rational number: Commutative property of rational numbers holds
true for addition and multiplication but does not hold true for subtraction and division.

It means that if p1/q1 and p2/q2 are any two rational numbers, then according to commutative
property of rational numbers, we mean that :

P1/q1 + p2/q2 = p2/q2 + p1/q1

P1/q1 * p2/q2 = p2/q2 * p1/q1

P1/q1 - p2/q2 <> p2/q2 - p1/q1

P1/q1 ÷ p2/q2 <> p2/q2 ÷ p1/q1

3. Additive Identity of Rational numbers: According to additive identity property, If we have a
rational number p/q, then there exist a number zero (0), such that if we add the number zero
to any number, the result remains unchanged. So we write it as : p/q + 0 = p/q

4. Multiplicative identity of Rational numbers: According to multiplicative identity property of
rational numbers, If we have a rational number p/q, then there exist a number one (1), such
that if we multiply the number one to any number, the result remains unchanged. So we write
it as : p/q * 1 = p/q

5. Power of zero: By the property Power of zero, we mean that there exists a number zero,
such that if we multiply zero to any rational number, then the product id zero itself. So if we
have p/q as a rational number, then we say: p/q * 0 = 0 .

6. Associative property of Rational numbers: Associative property of rational numbers holds
true for addition and multiplication but does not hold true for subtraction and division.

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It means that if p1/q1 , p2/q2 and p3/q3 are any three rational numbers, then according to
associative property of rational numbers, we mean that :

(P1/q1 + p2/q2) + p3/q3 = P1/q1 + (p2/q2 + p3/q3 )

(P1/q1 * p2/q2) * p3/q3 = P1/q1 * (p2/q2 * p3/q3 )

(P1/q1 - p2/q2) - p3/q3 <> P1/q1 - (p2/q2 - p3/q3 )

(P1/q1 ÷ p2/q2) ÷ p3/q3 <> P1/q1 ÷ (p2/q2 ÷ p3/q3 )

7.Distributive property of multiplication over addition and subtraction of rational numbers holds
true, which states:

P1/q1 * ( p2/q2 + p3/q3) = (p1/q1 * p2/q2) + (p1/q1 * p3/q3)

P1/q1 * ( p2/q2 - p3/q3) = (p1/q1 * p2/q2) - (p1/q1 * p3/q3)

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Thank You

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