Question

Using rational numbers (),+), (*) verify the commutative and associative, properties (11 4 properties) and distributive propet property​

Answer 1

properties of rational numbers, we will consider here the general properties such as associative, commutative, distributive and closure properties, which are also defined for integers. Rational numbers are the numbers which can be represented in the form of p/q, where q is not equal to 0. Basically, the rational numbers are the fractions which can be represented in the number line.

The word rational has evolved from the word ratio. In general, rational numbers are those numbers that can be expressed in the form of p/q, in which both p and q are integers and q≠0. The properties of rational numbers are:

1. Closure Property
2. Commutative Property
3. Associative Property
4. Distributive Property
5. Identity Property
6. Inverse Property

Closure property::

For example:

(7/6)+(2/5) = 47/30

(5/6) – (1/3) = 1/2

(2/5). (3/7) = 6/35

Commutative Property::

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

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

Associative Property::

for addition: x+(y+z)=(x+y)+z

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

Distributive Property::

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

Identity Property::

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

Inverse Property::

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