Which of the following expression proves that integers are not closed under division?

1 \div 2 = \frac{1}{2}

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- 1 \div 1 = - 1

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- 8 \div 2 = - 4

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21 \div 7 = 3

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Solution

The correct option is A $1 \div 2 = \frac{1}{2}$
$1 \div 2 = \frac{1}{2}$
Integers are whole numbers in addition to the negatives of natural numbers.
$∴ \frac{1}{2}$ is not an integer where as $1$ and $2$ are both integers. Hence, proved that integers are not closed under division.

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Similar questions

\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{5}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}}

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5) \frac{2}{3} : \frac{3}{5}

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