Question

Consider two rational numbers 3/4 and 5/7 and show that the commutative property holds true for addition and multiplication, but not for subtraction and division.

Answer 1

Step-by-step explanation:

first we see commutative property for addition

a+b=b+a.........(1)

let a=3/4

b=5/7

Now according to (1) , we see

3/4+5/7=41/28 (which is a rational number)

5/7+3/4=41/28 (which is a rational number)

Now, we see commutative property for multiplication

ab=bc

(3/4)*(5/7)= 15/28 (which is a rational number)

(5/7)*(3/4)=15/28 (which is a rational number)

Now, we see commutative property for substraction

a-b=b-a

(3/4)-(5/7)=1/28

(5/7)-(3/4)=-1/28

a-b≠b-a

commutative property doesn't hold for substraction.

Now, we see commutative property for division

a/b=b/a

(3/4)/(5/7)=21/20

(5/7)/(3/4)=20/21

a/b≠b/a

commutative property doesn't hold for division.