Download properties of real numbers

PROPERTIES OF REAL NUMBERS
SAVE THESE INSTRUCTIONS: Cut out the boxes below. Match the “Property Name” with its “Algebraic Representation”
and “Example”. Use a glue stick to paste them into your math journal in a three column T-chart (Column width = 2-1/4”; Row
height = about 1-3/8” tall or 4 lines wide rule). Label the columns. Find the properties in your textbook.
PROPERTY NAMES:
Commutative
(A)
Commutative
(B)
Property of
Property of
Addition
(G)
Property of
Property of
Zero
Addition
(L)
Multiplication
(K)
Identity
Identity
(H)
(M)
of Equality
(Q)
Then ac = bc
a b

c c
(c  0)
a(b + c) = ab + ac
If
a=b
Then a + c = b + c
(a + b) + c = a + (b + c)
2 = 2 True
Property
Multiplication
Identity
Inverse
(I)
Property of
Property
Multiplication
of Addition
Subtraction
(N)
Property of
Multiplication
Multiplication
Property of
Property of
Equality
Equality
Inverse
(J)
Division
(O)
Property of
Equality
NUMERICAL EXAMPLES:
a+0=a
5 + (-5) = 0
3+7=7+3
3=3
-1 ∙ n = -n
2+x = 2+x
-x
-x
If a = b
Then
Distributive
(E)
Property of
Contradiction
ALGEBRAIC REPRESENTATION:
If a = b
Associative
(D)
Addition
Property
Property of -1
(P)
Addition
Associative
Property of
Multiplication
Multiplication
(F)
(C)
2
1 = 3 False
a + (-a) = 0
a+b=b+a
= 2
True
3∙7=7∙3
3+2=3+2
5=5
5
1
1
5
(6 ∙ 4) ∙ 5 = 6 ∙ (4 ∙ 5)
7=7
(24) ∙ 5 = 6 ∙ (20)
7-5=7-5
120 = 120
2=2
-35 ∙ 0 = 0
9∙1=9
PROPERTIES OF REAL NUMBERS
Instructions: Cut out the boxes below. Match the Property Name with its Algebraic and Numerical Representations.
Use a glue stick to paste them into your math journal in a three column T-chart. Use your textbook for help.
PROPERTY NAMES:
(A) Commutative
(B) Commutative
(C) Associative
Property of
Property of
Property of
Addition
Multiplication
Addition
(F) Multiplication
(G) Identity
(D) Associative
(E) Distributive
Property
Property
of Multiplication
(H) Identity
(I) Inverse
(J) Inverse
Property of
Property of
Property of
Property
Property of
Zero
Addition
Multiplication
of Addition
Multiplication
(K) Multiplication
(L) Addition
Property of -1
(P) Identity
(M) Subtraction
Property of
Property of
Property of
Equality
Equality
Equality
Equality
(Q) Contradiction
a∙0=0
NUMERICAL EXAMPLES:
2 = 2 True
x
=
-x
0
If a = b
Then
a b

c c
(O) Division
Property of
ALGEBRAIC REPRESENTATION:
(a ∙ b) ∙ c = a ∙ (b ∙ c)
(N) Multiplication
If a = b
-1 ∙ n = -n
Then ac = bc
=
x+3
3=3
-x
3+2=3+2
3
False
(6 + 4) + 5 = 6 + (4 + 5)
9+0=9
5=5
6∙1=6
6=6
(10) + 5 = 6 + (9)
6(3) = 6(3)
15 = 15
18 = 18
(c  0)
If
a=b
Then a - c = b - c
a
1
1
a
a+0=a
2+x = 2+x
-x
-x
2
a(b + c) = ab + ac
If
a=b
1 = 3 False
a∙b=b∙a
a+b=b+a
a + (-a) = 0
= 2
5
1
1
5
True
5(4 + 2) = 5∙4 + 5∙2
7=7
5(6) = 20 + 10
7-5=7-5
30 = 30
2=2
3∙7=7∙3
-35 ∙ 0 = 0
Then a + c = b + c
(a + b) + c = a + (b + c)
a∙1=a
(6 ∙ 4) ∙ 5 = 6 ∙ (4 ∙ 5)
(24) ∙ 5 = 6 ∙ (20)
120 = 120
5 + (-5) = 0
8=8
8 8

2 2
4=4
3+7=7+3
-1 ∙ 5 = -5
Name____________________Date____________Teacher_________
Properties of Real Numbers
Property
Name
Commutative
Property of
Addition
Commutative
Property of
Multiplication
Associative
Property of
Addition
Associative
Property of
Multiplication
Distributive
Property
Multiplication
Property of Zero
Identity Property
of Addition
Identity Property
of Multiplication
ALGEBRAIC
REPRESENTATION
NUMERICAL
EXAMPLES
Inverse Property
of Addition
Inverse Property
of Multiplication
Multiplication
Property of -1
Addition Property
of Equality
Subtraction
Property of
Equality
Multiplication
Property of
Equality
Division Property
of Equality
Identity
Contradiction
ALGEBRAIC REPRESENTATION:
If a = b
Then ac = bc
a+0=a
5 + (-5) = 0
3+7=7+3
3=3
-1 ∙ n = -n
2+x = 2+x
-x
-x
If a = b
Then
a b

c c
(c  0)
a(b + c) = ab + ac
If
a=b
Then a + c = b + c
(a + b) + c = a + (b + c)
NUMERICAL EXAMPLES:
2
1 = 3 False
a + (-a) = 0
a+b=b+a
= 2
3+2=3+2
5=5
True
5
3∙7=7∙3
1
1
5
(6 ∙ 4) ∙ 5 = 6 ∙ (4 ∙ 5)
7=7
(24) ∙ 5 = 6 ∙ (20)
7-5=7-5
120 = 120
2=2
-35 ∙ 0 = 0
9∙1=9
2 = 2 True
ALGEBRAIC REPRESENTATION:
If a = b
Then ac = bc
a+0=a
5 + (-5) = 0
3+7=7+3
3=3
-1 ∙ n = -n
2+x = 2+x
-x
-x
If a = b
Then
a b

c c
(c  0)
a(b + c) = ab + ac
If
a=b
Then a + c = b + c
(a + b) + c = a + (b + c)
2 = 2 True
NUMERICAL EXAMPLES:
2
1 = 3 False
a + (-a) = 0
a+b=b+a
= 2
True
3∙7=7∙3
3+2=3+2
5=5
5
1
1
5
(6 ∙ 4) ∙ 5 = 6 ∙ (4 ∙ 5)
7=7
(24) ∙ 5 = 6 ∙ (20)
7-5=7-5
120 = 120
2=2
-35 ∙ 0 = 0
9∙1=9