# Properties of Rational Numbers Worksheets

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```					       Properties of Rational Numbers Worksheets
Properties of Rational Numbers Worksheets

Let us first look at the properties of rational numbers in order to understand about the
rational numbers in details. Although many properties of rational numbers worksheet are
available online to understand the concept of rational numbers and its usage. We will take the
properties of rational numbers one by one:

1.    Closure Property of Rational numbers: We say that the closure property of rational
numbers holds true for the addition, subtraction, multiplication and division. It simply means
that if we have any two rational numbers say p1/q1 and p2/q2, then according to closure
property of Addition, the sum of any two rational numbers p1/q1 + p2/q2 is also a rational
number.

Also according to closure property of subtraction, the difference of the two rational numbers is
also a rational number, mathematically p1/q1 – p2/q2 is also a rational number.

Similarly closure property also holds true for the multiplication and the division operation of
the rational number, which states :

Know More About      How to solve for a rational number

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P1/q1 * p2/ q2 and p1/q1 divided by p2 / q2 are also rational numbers if we have p1/q1 and
p2/q2 as the rational numbers.

2. Commutative Property of Rational Numbers : If we have any two rational numbers say
p1/q1 and p2/q2, then we say that the commutative property holds true for the addition and
the multiplication of rational numbers, but does not holds true for the subtraction and division
of the rational numbers. Mathematically we say 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 divided by p2/q2 < > p2/q2 divided by p1/q1

3. By Associative Property of rational numbers, we mean that if p1/q1, p2/q2 and p3/q3 are
any three rational numbers, then we say that if the order of grouping in addition and
multiplication is changed, then the result is same. On the another hand the result does not
remains same in the case of subtraction and division. Let us look at the Associative Property
mathematically :

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

( p1/q1 - p2/q2 ) - p3 / q3 <> p1/q1 - ( p2/q2 - p3 / q3 )

Read  More About   Solving equations with rational numbers

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

( p1/q1 divided p2/q2 ) divided p3 / q3 = p1/q1 divided ( p2/q2 divided p3 /q3 )

4. Additive Identity 0, exist for the rational number p/q such that the number 0 is added to
the given number , the result is the number itself.

So we say mathematically p/q + 0 = p/q

5. Multiplicative Identity is one ( 1) : There exist a number 1, such that If we multiply 1 to any
of the rational numbers, the result is the original rational number itself. If we have any rational
number p/q , then we say that

p/q * 1 = p/q

6. The additive inverse of any number is the negative of the given rational number and the
multiplicative inverse of any number is reciprocal of any rational number.

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Thank You

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