Properties of Rational Numbers
Properties of Rational Numbers
Closure Property:
Whole numbers: Closed under addition and multiplication but not under subtraction and division.
Integers: Closed under addition, subtraction, and multiplication but not under division.
Rational numbers: Closed under addition, subtraction, and multiplication. Not closed under division if the denominator is 0.
Examples:
(5/3) + (2/3) = 7/3 (Rational number, so closed under addition)
(4/5) - (7/5) = -3/5 (Still a rational number, so closed under subtraction)
Page 3-4: Closure Property Continued
More examples of closure:
Multiplication: (2/3) × (4/5) = 8/15 (Rational number, so closed under multiplication)
Division: (5/7) ÷ (2/3) = (5/7) × (3/2) = 15/14 (Rational number, but if divided by 0, it is undefined).
Conclusion: Rational numbers follow closure property for addition, subtraction, and multiplication but not for division by zero.
Page 5-6: Commutativity
Commutative Property:
Addition: a + b = b + a
Example: (3/4) + (5/6) = (5/6) + (3/4)
Multiplication: a × b = b × a
Example: (2/5) × (7/3) = (7/3) × (2/5)
Not Commutative for Subtraction and Division:
Example: (4/5) - (2/3) ≠ (2/3) - (4/5)
Example: (5/7) ÷ (3/2) ≠ (3/2) ÷ (5/7)