Download 2-2

Lesson 2-2: Properties of Operations
PROPERTY
DEFINITION
Under a binary operation (+,
-, *, /) when every pair of
elements from the set
results in an element from
that set.
Closure
Date_____________
p.45 - 54
EXAMPLE
*Whole, rational and real are
closed under addition and
multiplication.
(2)(4)=8
7.8 + 4.8 = 12.6
*Integers, rational, and real are
closed under subtraction.
3–3=0
12.7 - 8.2 = 4.5
*Nonzero rational and nonzero
real numbers are closed under
division.
9/2 = 4.5
6/3 = 2
Commutative of
Addition
The order in which two
numbers are added can be
changed without changing
the sum.
Commutative of
Multiplication
The order in which two
numbers are multiplied can
be changed without changing
the product.
Associative of
Addition
Associative of
Multiplication
The way in which we group
numbers to be added does
not change the sum.
The way in which we group
numbers to be multiplied
does not change the
product.
PROPERTY
Distributive
Property
DEFINITION
The product of one number
times the sum of a second
and a third equals the
product of the first and
second numbers plus the
product of the first and
third numbers.
Identity
Element of
Addition
When zero is added to any
real number that number is
returned. (Zero is the
identity element.)
Identity
Element of
Multiplication
When one is multiplied by
any real number that
number is returned. (One is
the identity element.)
The opposite of any number.
**When two opposites are
Additive Inverse
added the result is the
identity element.
Multiplicative
**When two _________
Inverse or
are multiplied the result is
____________ the identity element.
Multiplicative
Any number multiplied by
Property of Zero
zero is always ________.
Date_____________
EXAMPLE
Date_____________
Name the property for each of the following.
Ex 1| 5  4  4  5
Ex 2| 3  4  5  3  4  5
Ex 3| 5  0  5
1
Ex 4|  4   1
4
Ex 5|
4  6  7  7  4  6
Ex 6| 3
3
 1  3.75
4
Ex 7| 3  5  7   3  5  7
Ex 8| 53  4  5  3  5  4
Ex 9| 5   5  0
Ex 10| 10  0  0
HW: p.54/41-42  Make flash cards for each of the 11 properties