Real Numbers, Revision Notes: Maharashtra Class 9 MATH, Mathematics Part I

Real numbers

Commutativity
- Whole numbers are commutative under addition and multiplication. However, they are not commutative under subtraction and division.
- Integers are commutative under addition and multiplication. However, they are not commutative under subtraction and division.
- Rational numbers:
  1. Rational numbers are commutative under addition.

Example:

$\frac{2}{3} + (\frac{- 3}{2}) = (\frac{- 3}{2}) + (\frac{2}{3}) = \frac{- 5}{6}$

Example :

$(\frac{3}{4}) - (\frac{5}{2}) = (\frac{- 7}{4})$ and $\frac{5}{2} - \frac{3}{4} = \frac{7}{4}$

$∴ (\frac{3}{4}) - (\frac{5}{2}) \neq (\frac{5}{2}) - (\frac{3}{4})$

Example:

$(\frac{3}{4}) \times (\frac{- 2}{6}) = (\frac{- 2}{6}) \times (\frac{3}{4}) = \frac{- 1}{4}$

2 ÷ 5 ≠ 5 ÷ 2

Associativity
- Whole numbers are associative under addition and multiplication. However, they are not associative under subtraction and division.
- Integers are associative under addition and multiplication. However, they ar…

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