Properties of Rational Numbers
Exploring closure, commutative, associative, and distributive properties under addition, subtraction, multiplication, and division.
Definition
Rational numbers follow specific algebraic properties under operations like addition, subtraction, multiplication, and division. These include closure, commutative, associative, distributive properties, and the existence of additive and multiplicative identities and inverses. These properties simplify complex arithmetic calculations.
Key formula
a + b = b + a (Commutative for addition)
Worked examples
Using the commutative property: 2/3 + 4/5 = 4/5 + 2/3.
Using the additive identity: 3/7 + 0 = 3/7.
Using the multiplicative inverse of 2/5, which is 5/2 such that (2/5) * (5/2) = 1.
Common mistakes
- • Applying commutative or associative properties to subtraction or division where they do not hold true.
- • Confusing the additive inverse (changing sign) with the multiplicative inverse (reciprocal).
Introduction to Rational Numbers
Rational Numbers
Representation on Number Line
Rational Numbers
Rational Numbers Between Two Rational Numbers
Rational Numbers
Algebraic Expressions and Equations
Linear Equations in One Variable
Solving Equations with Variables on Both Sides
Linear Equations in One Variable
Reducing Equations to Simpler Form
Linear Equations in One Variable