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Properties of real numbers
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Slide 1

THE NUMBER LINE

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

END SHOW

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Slide 2

Standard 6:

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:

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Slide 3

The number line

The number line

Standards 6, 25

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Slide 4

Standards 6, 25

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:

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Slide 5

Standards 6, 25

Standards 6, 25

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Slide 6

PROPERTIES OF REAL NUMBERS

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

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Slide 7

PROPERTIES OF REAL NUMBERS

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

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Slide 8

PROPERTIES OF REAL NUMBERS

PROPERTIES OF REAL NUMBERS

IDENTITY PROPERTY:

Addition:

a + 0 = 0 + a=a

5 + 0

= 0 + 5

1 + 0

= 0 + 1

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