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1.02 Properties
Notes
Name: _________________________________
Date: __________________ Period: ________
 PROPERTIES OF ADDITION
Properties
Addition
Multiplication
The sum of any two real
numbers is a unique real
number.
The product of any two real
numbers is a unique real
number.
The order in which two
numbers are added does not
change the sum.
The order in which two
numbers are multiplied does
not change the product.
The way three numbers are
grouped when adding does
not change the sum.
The way you group 3
numbers when multiplying
does not change the product.
The sum of a number and
zero (0) is the number.
The product of a number and
one (1) is the number.
The sum of a number and its
opposite is zero (0).
The product of a number and
its reciprocal is 1.
Closure
Property
Commutative
Property
Associative
Property
Identity
Property
Inverse
Property
How will I
remember?
How will I
remember?
Properties
Definition
Distributive
Property
A number outside parenthesis must be multiplied by
everything inside.
Practice with Properties of Addition
Practice with Properties of Multiplication
1. (3 + 4) + 7 = 3 + (4 + 7)
________________
1. a(b + c) = ab + bc
________________
2. 7 – 0 = 7
________________
2. 4 ● 3 = 12
________________
3. 2 + 5 = 5 + 2
________________
3. 7(6 + 7) = 7  6 + 7  7
________________
4. 2 + (–2) = 0
________________
4. 7 ● 1 = 7
________________
5. 5 + (1 + 3) = (5 + 1) + 3
________________
5. 3  7  7  3
________________
6. 4 + 10 = 14
________________
6. 4 
7. Which property is being demonstrated here?
1
1
4
7. Which property is being demonstrated here?
8●1=8
8 + (-8) = 0
A. Identity Property
B. Inverse Property
________________
C. Associative Property A.
B.
D. Closure Property
Identity Property
Inverse Property
C. Associative Property
D. Closure Property
8. Identify which addition property is demonstrated
below.
3+7=7+3
8. Identify which multiplication property is
demonstrated below.
A.
B.
A.
B.
commutative
distributive
C.
D.
associative
inverse
9. Identify which addition property is demonstrated
below.
( ab) c  a (bc )
commutative
distributive
commutative
distributive
C.
D.
associative
identity
10. Identify which addition property is demonstrated
below.
5+0=5
A.
B.
commutative
identity
C.
D.
associative
inverse
associative
inverse
9. Identify which multiplication property is
demonstrated below.
6●5=5●6
(7 + 11) + 9 = 7 + (11 + 9)
A.
B.
C.
D.
A.
B.
commutative
distributive
C.
D.
associative
identity
10. Identify which multiplication property is
demonstrated below.
1 2
 1
2 1
A.
B.
commutative
distributive
C.
D.
associative
inverse