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Rohit writes . What is wrong with his step?

Class 8Rational NumbersRational Numbers
  • ANothing is wrong — subtraction is commutative on rationals
  • BHe applied commutativity to subtraction; the left side is but the right side is
  • CHe should have used 27 as the common denominator
  • DHe used associativity where distributivity was needed

Step-by-Step Solution

, while . Swapping the two numbers is allowed for + and ×, never for − or ÷. The denominator 9 he used is already correct, so that is not where the error lies.
Answer: B) He applied commutativity to subtraction; the left side is but the right side is

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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