Question

write the six properties of additions of rational number with example​

Answer 1

Answer:

• 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:

     Example:  (7/6)+(2/5) = 47/30

• 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        

     Example:     2/5×3/7 =  3/7×2/5 = 6/35

• 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

• 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