Question

Write the properties name of rational number with example

Answer 1

Answer:

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: Closure Property. Commutative Property.

...

For example:

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

(5/6) – (1/3) = 1/2.

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

Answer 2

Step-by-step explanation:

$\huge\bf{\underline{\pink{ANSWER}}}$

→ What are the properties of rational numbers?

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:

• Closure Property
• Commutative Property
• Associative Property
• Distributive Property
• Identity Property
• Inverse Property

⠀⠀⠀⠀⠀⠀⠀⠀⠀

• 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. For example:

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

• (5/6) – (1/3) = 1/2
• (2/5). (3/7) = 6/35

- Do you know why division is not under closure property?

The division is not under closure property because division by zero is not defined. We can also say that except ‘0’ all numbers are closed under division.

⠀⠀⠀⠀⠀⠀⠀⠀⠀

• 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
• Subtraction is not commutative property i.e. a-b ≠ b-a.
• The division is also not commutative i.e. a/b ≠ b/a

⠀⠀⠀⠀⠀⠀⠀⠀⠀

• 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.

Example: 1/2 + (1/4 + 2/3) = (1/2 + 1/4) + 2/3

⇒ 17/12 = 17/12

And in case of multiplication;

1/2 x (1/4 x 2/3) = (1/2 x 1/4) x 2/3

⇒ 2/24 = 2/24

⇒1/12 = 1/12

⠀⠀⠀⠀⠀⠀⠀⠀⠀

• 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)

Example : 1/2 x (1/2 + 1/4) = (1/2 x 1/2) + (1/2 x 1/4)

LHS = 1/2 x (1/2 + 1/4) = 3/8

RHS = (1/2 x 1/2) + (1/2 x 1/4) = 3/8

Hence, proved