Question

Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

Answer 1

Answer:

1)Closure property

For two rational numbers say x and y the results of addition, subtraction and multiplication operations give a rational number. We can say that rational numbers are closed under addition, subtraction and multiplication. For example: (7/6)+(2/5) = 47/30.

2) No, rational numbers are not closed under division. For example, let us take two rational numbers 2 and 0. ... As a division of two rational numbers 2 and 0 is not a rational number, so the division of two rational numbers is not closed.

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Answer 2

It is said that we have to give example for rational numbers that are closed under addition, subtraction, multiplication and division

let

$\frac{1}{2 } and \: \frac{1}{3}$

be two rational numbers

1. closed property under addition let

$\frac{1}{2} \: and \: \frac{1}{3}$

belongs to R then addition of these two also belongs to R

$\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$

Hence it is closed under addition.

2.closed under subtraction

$\frac{1}{2} - \frac{1}{3} = \frac{1}{6}$

hence, it is closed under subtraction.

3. closed under multiplication

$\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$

Hence , it is closed under multiplication

4.closed under division

$\frac{1}{2} \div \frac{1}{3 } = \frac{1}{2} \times \frac{3}{1} = \frac{3}{2}$

It is closed under division.

It we took 0 as a number then the division is not possible that it will give

$\infty$

as a value.

Hence, with 0 it is not closed and without 0 it is closed.

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