Transcript Section 1.5 Properties of Real Numbers

Properties of Real
Numbers
1. Objective: To apply the properties of
operations.
2. Commutative Properties
3. Associative Properties
4. Identity Properties
5. Inverse Properties
6. Distributive Property
On Tab 2: Commutative Properties
Changing the order of the numbers in addition
or multiplication will not change the result.
 Commutative Property of Addition states:
2+3=3+2
or
a+b=b+a
 Commutative Property of Multiplication states:
4•5=5•4
or
a • b = b • a.
On Tab 3: Associative Properties
Changing the grouping of the numbers in addition or
multiplication will not change the result.
Associative Property of Addition states:
3 + (4 + 5) = (3 + 4)+ 5
or
a + (b + c) = (a + b)+ c
Associative Property of Multiplication states:
(2 • 3) • 4 = 2 • (3 • 4)
or
(a • b) c = a (b • c)
On Tab 4: Identity Properties
Adding zero to a number does not change its
value.
2+0=2
a+0=a
&
&
0+2=2
0+a=a
Multiplying a number by 1 does not change
the value of the number.
5∙1=5
a∙1=a
& 1∙ 5=5
& 1∙a=a
On Tab 5: Inverse Properties
Opposites add to zero.
3 + -3 = 0
a + (-a) = 0
A number multiplied by its reciprocal is
always 1.
1 6 1 6
6    1
6 2 6 6
1 a 1 1a
a    1
a 1 a 1a
On Tab 6: Distributive Property
Multiplication distributes over addition &
subtraction.
32  5   3  2  3  5
ab  c   a  b  a  c
Let’s play
“Name that property!”
State the property or properties
that justify the following.
3+2=2+3
Commutative Property
State the property or properties
that justify the following.
10(1/10) = 1
Inverse Property of
Multiplication
State the property or properties
that justify the following.
3(x – 10) = 3x – 30
Distributive Property
State the property or properties
that justify the following.
3 + (4 + 5) = (3 + 4) + 5
Associative Property
State the property or properties
that justify the following.
(5 + 2) + 9 = (2 + 5) + 9
Commutative Property
2.
3+7=7+3
Commutative
Property of Addition
3.
8+0=8
Identity Property of
Addition
5.
6•4=4•6
Commutative Property
of Multiplication
11.
5•1=5
Identity Property of
Multiplication
21.
a + (-a) = 0
Inverse Property of
Addition
Properties of Real
Numbers
1. Objective: To apply the properties of
operations.
2. Commutative Properties
3. Associative Properties
4. Identity Properties
5. Inverse Properties
6. Distributive Property