Question

show all the properties of rational number for multiplication in tabular form:
( closure, commutative, multiplicative inverse, associative, distributive)​

Answer 1

closure

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

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

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

ational 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

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