# Properties of real numbersPage 2

#### WATCH ALL SLIDES

3.6 + 0

= 0 + 3.6

Multiplication:

For any real numbers a, b, and c:

= 9

= 4

= 6.4

= 5

= 1

= 3.6

Standards 6, 25

Slide 9

PROPERTIES OF REAL NUMBERS

INVERSE PROPERTY:

a + (-a) = (-a) + a=0

5 + (-5)

= (-5) + 5

3 + (-3)

= (-3) + 3

3.6 + (-3.6)

= (-3.6)+ 3.6

Multiplication:

For any real numbers a, b, and c:

= 1

= 1

= 1

= 0

= 0

= 0

Standards 6, 25

Slide 10

PROPERTIES OF REAL NUMBERS

DISTRIBUTIVE PROPERTY:

Distributive:

For any real numbers a, b, and c:

a(b+c) = ab + ac

(b+c)a = ba + ca

and

3(5+1) = 3(5) + 3(1)

(5+1)3 = 5(3) + 1(3)

and

4(2+6) = 4(2) + 4(6)

(2+6)4 = 2(4) + 6(4)

and

Standards 6, 25

Slide 11

Name the property shown at each equation:

Identity property (X)

Commutative property (+)

Inverse property (+)

Distributive property

Associative property (+)

Commutative property (X)

Standards 6, 25

Slide 12

Simplify 3(4c -7d) + 5(2c + 9c)

3(4c -7d) + 5(2c + 9d)

= 3(4c) – 3(7d) +5(2c) +5(9d)

=12c – 21d + 10c +45d

= 12c + 10c – 21d + 45d

= 22c +24d

Use distributive property

Multiply

Use commutative property to group like terms

= 3 – x + 9x -6

= 3 -6 - x + 9x

= 8x-3

Use distributive property

Multiply

Use commutative property to group like terms

Add like terms and commutative property

Standards 6, 25