Properties of real numbers

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Slide 1

THE NUMBER LINE

AND

NUMBER SYSTEMS

Standards 6, 25

PROPERTIES OF REAL NUMBERS

PROPERTIES OF REAL NUMBERS

EXAMPLES OF PROPERTIES

OF REAL NUMBERS

SIMPLIFYING EXPRESSIONS

APPLYING PROPERTIES

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Slide 2

Standard 6:

Students add, subtract, multiply, and divide complex numbers.

Estándar 6:

Los estudiantes suman, restan, multiplican, y dividen números complejos.

Standard 25:

Students use properties from number systems to justify steps in combining and simplifying functions.

Estándar 25:

Los estudiantes usan propiedades de los sistemas numéricos para justificar pasos al combinar y simplificar funciones.

ALGEBRA II STANDARDS THIS LESSON AIMS:

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Slide 3

The number line

Standards 6, 25

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Slide 4

Standards 6, 25

RATIONAL NUMBERS:

where:

m and n are integers.

0.25

0.75

7

10

IRRATIONAL NUMBERS

-8

0

None can be expressed as a fraction!

The following numbers can be expressed as fractions and therefore they are Rational numbers:

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Slide 5

Standards 6, 25

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Slide 6

PROPERTIES OF REAL NUMBERS

COMMUTATIVE PROPERTY:

Addition:

a + b = b + a

5 + 7

= 7 + 5

1 + 6

= 6 + 1

3.6 + 1.1

= 1.1 + 3.6

Multiplication:

For any real numbers a, b, and c:

Standards 6, 25

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Slide 7

PROPERTIES OF REAL NUMBERS

ASSOCIATIVE PROPERTY:

Addition:

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

(3 + 4) +1

= 3 + (4 + 1)

(2 + 5) + 7

= 2 + (5 + 7)

(6.2 + 4.1) +3.3

= 6.2 + (4.1 + 3.3)

Multiplication:

For any real numbers a, b, and c:

Standards 6, 25

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Slide 8

PROPERTIES OF REAL NUMBERS

IDENTITY PROPERTY:

Addition:

a + 0 = 0 + a=a

5 + 0

= 0 + 5

1 + 0

= 0 + 1