Question

mention the properties of Ration -nal number and write their general form​

Answer 1

A Rational Number is a number that can be written in the form of p/q where p, q are integers, and q ≠ 0. You can learn about the General Properties of Rational Numbers like Closure, Commutative, Associative, Distributive, Identity, Inverse, etc.

Answer 2

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Properties of rational numbers:

1. Closure Property

For two rational numbers say x and y the results of addition, subtraction and multiplication operations give a rational number. We can say that rational numbers are closed under addition, subtraction and multiplication.

2. Commutative Property

For rational numbers, addition and multiplication are commutative.

Commutative law of addition: a+b = b+a

Commutative law of multiplication: a×b = b×a

3. Associative Property

Rational numbers follow the associative property for addition and multiplication.

Suppose x, y and z are rational, then for addition: x+(y+z)=(x+y)+z

For multiplication: x(yz)=(xy)z.

4. Distributive Property

The distributive property states, if a, b and c are three rational numbers, then;  

a x (b+c) = (a x b) + (a x c)

5. Identity Property

0 is an additive identity and 1 is a multiplicative identity for rational numbers.

Examples:

1/2 + 0 = 1/2    [Additive Identity]

1/2 x 1 = 1/2   [Multiplicative Identity]

6. Inverse Property

For a rational number x/y, the additive inverse is -x/y and y/x is the multiplicative inverse.

Examples:

The additive inverse of 1/3 is -1/3. Hence, 1/3 + (-1/3) = 0

The multiplicative inverse of 1/3 is 3. Hence, 1/3 x 3 = 1

General form: A number that can be expressed in the form $\frac{p}{q}$ , where p and q are  integers and q ≠ 0, is called a rational number.

General form:  $\frac{p}{q},where \: q\neq 0.$

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