Question

Write the properties of rational numbers of addition,subtraction, multiplication and division.


PLEASE TELL ME FAST IT IS VERY URGENT

​

Answer 1

Answer:

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

For example:

Commutative law example

Subtraction is not commutative property i.e. a-b ≠ b-a. This can be understood clearly with the following example:

Commutative law - subtraction LHS

Whereas

Commutative law - subtraction RHS

The division is also not commutative i.e. a/b ≠ b/a, since,

Commutative law - Division LHS

Whereas,

Commutative law - Division RHS

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

Identity and Inverse Properties of Rational Numbers

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]

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

Answer 2

Given : rational numbers

To find  : compare the properties of rational numbers in in addition subtraction multiplication and division with examples​

Solution:

Addition of 2 rational numbers is a rational number

1/2  + 1/3  =  5/6

Subtraction of 2 rational numbers is a rational number

1/2  - 1/3  = 1/6

multiplication of 2 rational numbers is a rational number

(1/2) * (1/3)  = 1/6

Division  of 2 rational numbers is a rational number  

Except in the case when divisor = 0

(1/2) ÷ (1/3)  =    3/2

(1/2)  ÷ 0 =  ∞

0  ÷ 0 = undefined

Addition and Multiplication follows commutative and associative property

but Subtraction and Division does not follow

1 + 2 = 2 + 1  = 3    while  1  - 2  ≠ 2 -  1

1  * 2  = 2 * 1  = 2      while    1 /2  ≠  2/1

(1 + 2) + 3 = 1 + (2 + 3)  = 6        (1 - 2) - 3 ≠  1 - ( 2 - 3)

(1 * 2 ) *  3 = 1  * (2  * 3) = 6       (1 ÷ 2) ÷ 3 ≠ 1  ÷ ( 2 ÷ 3)

Learn More:

write a rational number which does not lie between the rational ...

brainly.in/question/8301628

3/7 line between (a) 4/9,5/9

brainly.in/question/14752046