- AClosure under multiplication
- BCommutativity
- CAssociativity
- DDistributivity
Step-by-Step Solution
Closure means multiplying two rationals always gives a rational; is rational.
Answer: A) Closure under multiplication
Which property guarantees that is again a rational number?
Class 8Rational NumbersRational Numbers
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).
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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