Question

1)Take two examples of rational numbers and verify all the properties that are satisfied in rational numbers

Answer 1

2/3 and 5/7 are rational number because it is in the form of p/q and q does not 0.....

Answer 2

Answer: Verified.

Step-by-step explanation:  We are given to verify all the properties of rational numbers by taking any two rational numbers as example.

We know that a rational number is of the form $\dfrac{p}{q},~q\neq 0$ and p, q are integers.

So, let the two rationals be $\dfrac{1}{2},~~\dfrac{3}{2}.$

The properties are as follows:

(i) Closure property : Addition and multiplication of two rational numbers is again a rational number.

We have

$\dfrac{1}{2}+\dfrac{3}{2}=2,~\textup{a rational},\\\\\dfrac{1}{2}\time\dfrac{3}{2}=\dfrac{3}{4},~\textup{a rational}.$

(ii) Commutative property : Addition and multiplication of rational numbers is commutative.

We have

$\dfrac{1}{2}+\dfrac{3}{2}=2=\dfrac{3}{2}+\dfrac{1}{2},\\\\\dfrac{1}{2}\times\dfrac{3}{2}=\dfrac{3}{4}=\dfrac{3}{2}\times\dfrac{1}{2}.$

(iii) Associative property.

(iv) Distributive property.

One can also verify the last two properties because by taking a third rational number.

Hence completed.