Which statement is correct about division of rational numbers?

Class 8Rational NumbersRational Numbers

ADivision is closed on rationals if we exclude division by 0
BDivision is commutative on rationals
CDivision is associative on rationals
DEvery rational divided by 0 gives 0

Step-by-Step Solution

Dividing one rational by a non-zero rational gives a rational, so division is closed (excluding 0). It is neither commutative nor associative.

Answer: A) Division is closed on rationals if we exclude division by 0

Key idea: Closure of rationals

Rationals are **closed under addition, subtraction, and multiplication** — the result is always rational.

But **division is closed only if you exclude division by 0**: for any rationals a and b ≠ 0, a ÷ b is rational.

This is more than integers (which weren't closed under division at all) and more than fractions (which sometimes had subtraction lead outside the fractions). Rationals form the smallest 'nice' number system that supports all four basic operations (with the 0-divisor exception).

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