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# Properties Of Rational Numbers

Rational numbers are terminating or recurring decimal numbers written in the form of fraction $\frac{p}{q}$ in which 'p' and 'q' are integers and the denominator 'q' not equal to zero.

Let a,b,c be three Rational Numbers and the Properties of Rational Numbers are given below:
1. Rational numbers are commutative and associative under addition and multiplication.
Commutative law:
a + b = b + a
a x b = b x a
Associative law:
a + (b + c) = (a + b) + c
a x (b x c) = (a x b) x c

2. Rational numbers holds true for closure law under addition, subtraction and multiplication.
a + b = a rational number
a - b = a rational number
a x b = a rational number
a / b = not a rational number

3. Rational numbers have an additive identity of 0 and multiplicative identity of 1.
a + 0 = a
a x 1 = a

4. Rational numbers hold true for distributive property also.
a + (b x c) = (a + b) x (a + c)
(a + b) x c = (a x c) + (b x c)

5. If the product of two rational number is 1 then the rational number is multiplicative inverse of the other.

## Identity Property of Rational Numbers

Rational numbers are the numbers which can be expressed in the form x/y, provided y is not equal to zero and x,y are integers. Apart from the addition, subtraction, multiplication and division, rational numbers show a specific property which is called identity of Rational Numbers and such numbers are called identity property of rational numbers.

## Distributive Property of Rational Number

Rational numbers are those numbers that can be expressed in the form of p/q, in which 'p' and 'q' both are Integer numbers, where value of 'q' can never be equal to the zero i.e. (q ≠ 0). Do you know distributive property of Rational Numbers? This is an important property for applying any particular operation on the rational numbers. The distr...Read More

## Inverse Property of Rational Numbers

Before we start with inverse property, let's recall some concepts about the Rational Numbers. Rational numbers are the Ratio of two integers. In other words, we can say that if two integers are stated as a ratio than the resulting number is Rational number.

Inverse Property of rational number states that the multiplication of rational nu...Read More

## Commutative Property of Rational Numbers

Rational numbers follow Commutative Property rule, according to which we can say that if we have two Rational Numbers a/b and c/d then addition of that fallows commutative additions. The commutative addition can be represented as a/b +c/d =c/d +a/b.

It will be more be clear with the help of an example:

## Associative Property of Rational Numbers

In mathematical world, Associativity is an equity of some binary applications. It states that, within a problem or in a Mathematical Expression having two or more appearances in a sequential manner or in a row of the similar associative operator, the sequence in which the applications are performed does not matter until the sequence of o...Read More

## Closure Property of Rational Numbers

Rational numbers shows one of the important property called as closure property. According to closure property, two Rational Numbers say Q and Z are said to be closed if we perform some operation on these numbers and the answer is also a rational number. Rational numbers are closed under addition, subtraction, multiplication and division ...Read More

## Additive Inverse of Rational Numbers

Any Integer  in (a/b)form where, 'b' is not  equal  to '0' is defined as rational number. In this 'a' and 'b' are integers and if  b> 0 than every integer is called as rational number. Rational number posses lot's of properties one of them is additive inverse of Rational Numbers. Additive inverse means  addition  of inverse or addition of negative or ...Read More

## Multiplicative Inverse of Rational Numbers

Let's discuss about the multiplicative inverse of Rational Numbers. Simply the multiplicative inverse is the reciprocal of a fraction like multiplicative inverse of 'm/n' is 'n/m'. The reciprocal or multiplicative inverse for a number z is denoted by 1/z or z-1. In rational numbers, zero does not have a reciprocal because no rationa...Read More

## Reciprocal of Rational Numbers

Rational numbers are the numbers expressed as the Ratio of the two integers. The basic rational number is expressed in the form of (p/q), where 'p' and 'q' are two integers. Let us see some example of Rational Numbers:-

2/3,

1/2,

11/17.

Reciprocal of the rational numbers can be defined as the reverse of the rational numbers, ...Read More

## Equivalent Rational Numbers

Equivalent Rational Numbers are those numbers which have same value but are represented in different ways. The same concept can also be defined as, the equivalence of Fractions in mathematics and the numbers giving same ratio. The ratios of the two numbers have same or equivalent ratios for the ratios of the two different numeric values. To unders...Read More

## Standard Form of a Rational Number

The standard form of a rational number is the Ratio or division of an Integer called the numerator by a positive integer called denominator and can be written in form of (numerator/ denominator) or a/b, where a is any integer and b is a denominator with positive integer (denominator is not equal to zero,b≠0). Let’s take some example to unde...Read More