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Compute and . What do the two answers show?

Class 8Rational NumbersRational Numbers
  • ABoth are , so division is commutative
  • BThey are and , so division is not commutative
  • CThey are and , so division is not associative
  • DBoth are , so division is closed

Step-by-Step Solution

, while . Swapping the order turned the answer into its reciprocal, so division is not commutative. The trap is saying "not associative" — associativity is about regrouping THREE numbers, which two numbers cannot test.
Answer: B) They are and , so division is not commutative

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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