FOU-PR Classification & Properties of Real Numbers

natural numbers

example: 1, 2, 3, 4, 5, 6, 7, 8, ...

- also called "counting numbers"

- no fractions

- no decimals

whole numbers

example: 0, 1, 2, 3, 4, 5, 6, 7, 8, ...

- add zero to the natural numbers

- no fractions

- no decimals

integers

example: ... -3, -2, -1, 0, 1, 2, 3, ...

- no fractions

- no decimals

- includes positive and negative numbers

rational numbers

examples: 1/2 .3 √9

- numbers that can be made into a fraction

- will appear as terminating or repeating decimal

irrational numbers

examples: √8 π √3

- number that cannot be made into a fraction

- decimals that are non-terminating or non-repeating

real numbers

any number you can think of

- includes all rational and irrational numbers

Commutative Property of Addition

a + b = b + a

example: 5 + 6 = 6 + 5

Associative Property of Addition

(a + b) + c = a + (b + c)

example: (9 + 2) + 5 = 9 + (2 + 5)

Commutative Property of Multiplication

a • b = b • a

example: 2 • 5 = 5 • 2

Associative Property of Multiplication

(a • b) • c = a • (b • c)

example: (2 • 5) • 9 = 2 • (5 • 9)

Identity Property of Multiplication

a • 1 = a

example: 5 • 1 = 5

Zero Property of Multiplication

a • 0 = 0

example: 1,732 • 0 = 0

Distributive Property

a(b + c) = a • b + a • c

example: 3(1 + 4)= (3 • 1) + (3 • 4)

Identity Property of Addition

a + 0 = a

example: 84 + 0 = 84

inverse operations

operations that "undo" each other

Multiplicative Inverse

reciprocal

example: The reciprocal of 3 is 1/3 because when multiplied together they equal one: 3 • (1/3) = 1