# Real Numbers Worksheet

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Real Numbers
Definition: The union of the rational numbers and the irrational numbers is the set of real
numbers.
The sets that make up the real numbers are called subsets of the real numbers
Properties of Real numbers:
Addition:
1.
For all real a, b
a + b = b + a
Commutative:
2.
For all real a, b, c
a + (b + c) = (a + b) + c
Associative:
3.
There exists a real number 0 such that for every real a
a + 0 = a
Identity:
4.
For every real number a there exist a real number, denoted
Additive Inverse (Opposite):
(a), such that a + (–a) = 0
Multiplication:
1.
For all real a, b
ab = ba
Commutative:
2.
For all real a, b, c
(ab)c = a(bc)
Associative:
3.
There exists a real number 1 such that for every real a
a × 1 = a
Identity:
4.
For every real number a except 0 there exist a real
Multiplicative Inverse (Reciprocal):
number, denoted , such that a × = 1
Distributive Law
For all real a, b, c
a(b + c) = ab + ac, and (a + b)c = ac + bc.
Part 5: Exponents and Scientific Notation
0 :
Exponents properties (
(product rule)
1.

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