Which of the following satisfies closure property?

3 + 4 = 7

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5 + 6 = 11

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10 + 2 = 12

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all of these

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Solution

The correct option is D all of these
For any two whole numbers a and b, (a + b) is also a whole number. This is called the Closure-Property of Addition.
$3$ and $4$ are whole numbers
$3 + 4 = 7$
$7$ is also whole number.
Similarly, it is true for all whole numbers.
Thus the answer is all of these.

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\frac{2 \times 6}{2} = \frac{8}{2} + \frac{4}{2}

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

If $\frac{4}{5} \div \frac{- 2}{3}$ follows closure property of division then the resultant number ____ is a Rational number.

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