Real Numbers and their Properties

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Presentation transcript:

Real Numbers and their Properties 5.5 Real Numbers and their Properties

Real Numbers The set of real numbers is formed by the union of the rational and irrational numbers. The symbol for the set of real numbers is

Relationships Among Sets Irrational numbers Rational numbers Integers Whole numbers Natural numbers Real numbers

Properties of the Real Number System Closure If an operation is performed on any two elements of a set and the result is an element of the set, we say that the set is closed under that given operation.

Commutative Property Addition a + b = b + a for any real numbers a and b. Multiplication a • b = b • a for any real numbers a and b.

Example 8 + 12 = 12 + 8 is a true statement. Note: The commutative property does not hold true for subtraction or division.

Associative Property Addition (a + b) + c = a + (b + c), for any real numbers a, b, and c. Multiplication (a • b) • c = a • (b • c), for any real numbers a, b, and c.

Example (3 + 5) + 6 = 3 + (5 + 6) is true. Note: The associative property does not hold true for subtraction or division.

Distributive Property Distributive property of multiplication over addition a • (b + c) = a • b + a • c for any real numbers a, b, and c. Example: 6 • (r + 12) = 6 • r + 6 • 12 = 6r + 72

Homework P. 256 # 2 – 80 even