## mention the communicative associative and distributive property of rational number also check a x b = b x a and a + b =b + A for a

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mention the communicative associative and distributive property of rational number also check a x b = b x a and a + b =b + A for a =1/2 and b=3/4​

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1 month 2021-08-16T03:59:03+00:00 1 Answers 0 views 0

Step-by-step explanation:

1. Commutativity- Rational numbers are commutative under addition and multiplication. If p and q are two rational numbers, then:

Commutative law under addition says- p + q = q + p.

Commutative law under multiplication says p x q = q x p.

Note- Rational numbers, integers and whole numbers are commutative under addition and multiplication. Rational numbers, integers and whole numbers are non commutative under subtraction and division.

2.Associative Property

Suppose x, y and z are rational, then for addition: x+(y+z)=(x+y)+z

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

3.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

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