# Closure Property Of Rational Numbers

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```					      Closure Property Of Rational Numbers
Closure Property Of Rational Numbers

Rational numbers are the numbers which can be expressed in the form of p/q, where p and q
are the integer numbers and q <> 0. There is a big list of Properties of rational numbers.
Some of them are:
1. Identity Property of Rational Numbers.

2.    Commutative property of rational numbers.

3.    Associative property of rational numbers.

4.    Closure Property of Rational Numbers.

5.    Dense property of rational numbers.

6.    Property of zero.

Here we will study about Closure Property of Rational Numbers:

Know More About Discovery Of Irrational Numbers

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Any two rational numbers say p1/q1 and p2/q2 are said to be closed under different
mathematical operations if the resultant rational number is also a rational number.

The rational numbers are closed under addition, subtraction, multiplication and division by
nonzero rational numbers.

Let us study it in more detail:

Closure property of rational numbers under Addition: Any two rational numbers say p1/q1 and
p2/q2 are said to be closed under addition as we observe that the sum of (p1/q1) + (p2/q2) is
also a rational number.

Let us take p1/q1 =3/6 and p2/q2 as 2/5, then 3/6    + 2/5 = (15 + 12) / 30 = 27/30, which is
again a rational number.

Thus we conclude that closure property of Addition holds true for rational numbers.

Closure property of rational numbers under subtraction: Any two rational numbers say p1/q1
and p2/q2 are said to be closed under addition, as we observe that the difference of these two
rational numbers ( p1/q1) - ( p2/q2 ) is also a rational number.

Let us take p1/q1 =3/6 and p2/q2 as 2/5, then 3/6 - 2/5 = ( 15 - 12 ) / 30 = 2/30, which is
again a rational number.

Thus we conclude that closure property of subtraction holds true for rational numbers.

Closure property of rational numbers under Multiplication: Any two rational numbers say p1/q1
and p2/q2 are said to be closed under multiplication, as we observe that the product of (p1/q1)
* (p2/q2) is also a rational number.

Let us take p1/q1 =3/6 and p2/q2 as 2/5, then 3/6 * 2/5 = ( 3 * 2 )/ (6 * 5 ) = 6/30, which is
again a rational number.
Read  More About Differential Calculus

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Thus we conclude that closure property of Multiplication holds true for rational numbers.

Closure property of rational numbers under division: Any two rational numbers say p1/q1 and
p2/q2 are said to be closed under division, as we observe that the quotient of (p1/q1) ÷
(p2/q2) is also a rational number.

Let us take p1/q1 =3/6 and p2/q2 as 2/5, then 3/6     ÷ 2/5 = (3/6) * (5/2)   = 15/12, which is
again a rational number.

Thus we conclude that closure property of Division holds true for rational numbers.

So we come to the conclusion that the closure property of rational numbers holds true for all
the mathematical operators.

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Thank You

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