Download Section 1.5 Properties of Real Numbers

Properties of Real Numbers
Commutative
Associative
Distributive
Identity + ×
Inverse + ×
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
ab = ba.
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
(ab)c = a(bc)
Distributive Property
Multiplication distributes over addition.
ab  c   ab  ac
32  5  3  2  3  5
Additive Identity Property
There exists a unique number 0 such
that zero preserves identities under
addition.
a + 0 = a and 0 + a = a
In other words adding zero to a
number does not change its value.
Multiplicative Identity Property
There exists a unique number 1 such
that the number 1 preserves identities
under multiplication.
a ∙ 1 = a and 1 ∙ a = a
In other words multiplying a number
by 1 does not change the value of the
number.
Additive Inverse Property
For each real number a there
exists a unique real number –a
such that their sum is zero.
a + (-a) = 0
In other words opposites add to
zero.
Multiplicative Inverse Property
For each real number a there exists a
unique real number
product is 1.
1
a 1
a
1
a
such that their
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
Multiplicative Inverse Property
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
25.
1
5/
+
0
=
7
1
5/
7
Identity Property of
Addition
40.
a + (-a) = 0
Inverse Property of
Addition
Properties of Real Numbers
Commutative
Associative
Distributive
Identity + ×
Inverse + ×