Question

The property satisfied by the division of whole numbers is

• A. Closure property
• B. Commutative property
• C. None of these
• D. Associative property

Answer 1

Answer: (C)

Division of whole numbers does not satisfy any of the properties.

i) Let the divisor be $0$.

$\frac{a}{0}$ is not defined for any whole number $a$

$\frac{a}{0}$ is not a whole number $⟹$ whole numbers are not closed under division.

ii) Consider any 2 whole numbers, say, $6$ and $3$, $\frac{6}{3}=2$ $\ne$ $\frac{3}{6}=0.5$ $⟹$ division of whole numbers is not commutative

iii)Consider any 3 whole numbers, say, $2,4,8$.

$\frac{\frac{2}{4}}{8}=\frac{1}{16}$ and $\frac{2}{\frac{4}{8}}=4$, i.e

$\frac{\frac{2}{4}}{8}\ne \frac{2}{\frac{4}{8}}$ $⟹$ division of whole numbers is not assocoative