Question

Mention the commutativity,associative and distrbutive properties of rational numbers. Also check a×b=b×a for a= 1/2 and b=3/4 ​

Answer 1

Step-by-step explanation:

COMMUTATIVE PROPERTY=a+b=b+a

let a=3 ; b=2

L.H.S=a+b

=3+2

=5

R.H.S=b+a

=2+3

=5

Here L.H.S=R.HS

THEREFORE, PROPERTY is verified.

ASSOCIATIVE PROPERTY=(a+b)+c=a+(b+c)

let a=3 ; b=2 ;c=5

L.H.S=(a+b)+c

=(3+2)+5

=5+5

=10

R.H.S=a+(b+c)

= 3+(2+5)

= 3+7

= 10

Here L.H.S=R.H.S

THEREFORE, ASSOCIATIVE PROPERTY is verified

DISTRIBUTIVE PROPERTY OF RATIONAL NUMBERS=a/b×c/d=c/d×a/b

let a/b=3/2 ; c/d=8/7

L.H.S=a/b × c/d

= 3/2×8/7

=12/7

R.H.S=c/d × a/b

= 8/7×3/2

=12/7

Here,L.H.S=R.H.S

THEREFORE, DISTRIBUTIVE PROPERTY is verified.

QUESTION-a×b=b×a for a= 1/2 and b=3/4

L.H.S=a×b

=1/2×3/4

=3/8

R.H.S=b×a

=3/4×1/2

=3/8

Here L.H.S = R.H.S

HENCE VERIFIED.