Algebraic Properties of Real Numbers
The basic algebraic properties of real numbers a,b and c are:
1. Closure: a + b and ab are real numbers2. Commutative: a + b = b + a, ab = ba
3. Associative: (a+b) + c = a + (b+c), (ab)c = a(bc)
4. Distributive: (a+b) c = ac+ bc
5. Identity: a+0 = 0+a = a
6. Inverse: a + (-a) = 0, a(1/a) = 1
7. Cancellation: If a+x=a+y, then x=y
8. Zero-factor: a0 = 0a = 0
9. Negation: -(-a) = a, (-a)b= a(-b) = -(ab), (-a)(-b) = ab
Algebraic Combination
Factors with a common denominator can be expanded:
Fractions can be added by finding a common denominator:
Products of fractions can be carried out directly:
Quotients of fractions can be evaluated by inverting and multiplying:
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