Properties of Real Numbers

2

PROPERTIES OF REAL NUMBERS

COMMUTATIVE PROPERTY:

•Addition: a + b = b + a5 + 7 = 7 + 5

1 + 6 = 6 + 1

3.6 + 1.1 = 1.1 + 3.6

•Multiplication:9 6

4 20

= 6 9

6.4 5.2

= 20 4

= 5.2 6.4

For any real numbers a, b, and c:

a b = b a

Standards 6, 25

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

3

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:

15 4

72

35

15 4

72

35

=

34 45 6 = 34 45 6

5.7 7.2 2.3 5.7 7.2 2.3=

a b c= a b c

Standards 6, 25

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

4

PROPERTIES OF REAL NUMBERS

IDENTITY PROPERTY:

•Addition: a + 0 = 0 + a=a5 + 0 = 0 + 5

1 + 0 = 0 + 1

3.6 + 0 = 0 + 3.6

•Multiplication:9 1

4 1

= 1 9

6.4 1

= 1 4

= 1 6.4

For any real numbers a, b, and c:

a 1 = 1 a = a = 9

= 4= 6.4

= 5

= 1= 3.6

Standards 6, 25

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

5

PROPERTIES OF REAL NUMBERS

INVERSE PROPERTY:

•Addition: 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

a = a = 1 1a

1a

If a=0 then

35

53

15

5

12

2 = 212

=53

35

15

= 5

Standards 6, 25

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

6

PROPERTIES OF REAL NUMBERS

DISTRIBUTIVE PROPERTY:

•Distributive:

For any real numbers a, b, and c:

a(b+c) = ab + ac (b+c)a = ba + caand

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

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

7

Name the property shown at each equation:

1 45 = 45a)

56 + 34 = 34 + 56b)

(-3) + 3 = 0c)

5(9 +2) = 45 + 10d)

(2 + 1) +b= 2 + (1 + b)e)

-34(23) = 23(-34)f)

Identity property (X)

Commutative property (+)

Inverse property (+)

Distributive property

Associative property (+)

Commutative property (X)

Standards 6, 25

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

8

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

Add like terms

Simplify 14

(12-4x) 35

(15x-10)+

14

(12-4x) 35

(15x-10)+ =( )(12) – ( )(4x) + ( )(15x) – ( )(10)14

14

35

35

= 3 – x + 9x -6

= 3 -6 - x + 9x

= 8x-3

Use distributive propertyMultiply

Use commutative property to group like terms

Add like terms and commutative property

Standards 6, 25

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved