Question

Take any four rational numbers in which 2 are positive and 2 are negative.

Verify them for all the properties given below:

a) Closure property b) Associative property

c) Distributive property d) Commutative property

And write your observations for the same.​

Answer 1

in commutative

addition: 1/2 +3/2 = 3/2+1/2

(3+1)/2 = (1+3)/2

Answer 2

commutative property = 3/8 *4/6=12/48=1/4 = 4/6 * 3/8 =12/48=1/4

commutative property [ negetive numbers] = -5/30 * -9/18=  45/540

                                                                         -9/18 * -5/30= 45/540

associative property= 3/8*4/6*1/2=1/2*4/6*3/8

associative property in negetive numbers=  -5/30 * -9/18 * -8/9= -8/9*-5/30 * -9/18

closure property = 3/8 *4/6 = 12/48 = 1/4

closure property [ negetive numbers]= -5/30 * -9/18=  45/540=12

[not satisfied]

distributive=  3/8[ 4/6 +1/2] =3/8 * 4/6 + 3/8 *1/2

                     negetive= -5/30 [ -9/18 +-8/9] = -5/30 * -9/18 + -5/30 * -8/9