5­3: Properties of Operations
What
Commutative
Property​
?
is
Addition:
a+b=b+a
Multiplication:
a(b) = b(a)
What
is
Associative
Property​
?
the
Additive Identity​
:
Multiplication
Identity​
:
Addition:
a + (b + c) = (a + b) + c
Multiplication:
a(b∙c) = (a∙b)c
a+0=a
a∙1=a
The ​
commutative
property ​
states that
the order in which
numbers are added
or multiplied does
not change the sum
or product.
The
associative
​
property ​
states that
the way in which
numbers
are
grouped when they
are
added
or
multiplied does not
change the sum or
product.
When 0 is added to
any number, the
sum is the number.
When the number
is multiplied by 1,
the product is the
number.
Multiplicative
Property of Zero​
:
Example 1a:
Page 368
a∙0=0
When any number
is multiplied by 0,
the product is 0.
Name
the 1.
Name
property shown in property.
the statement:
a) 4​
2 + x + y = 42 + y +
the
x
What
is
Counterexample​
?
Example 2c:
Page 369
15 ÷ 3 = 3 ÷ 15
If you find a
counterexample​
, an
example that shows
that a conjecture is
false, the property
does not apply.
State whether the
following conjecture 1. True or false?
is true or false. If 2.
Write
an
false, provide a
example to show it.
counterexample.
The difference of two
different whole numbers
is always less than both
of the two numbers.
Summary:
Example 3d:
Page 369
Lance made four
phone calls from
his cell phone
today. The calls
lasted 4.7, 9.4, 2.3,
and 10.6 minutes.
Use mental math to
find
the
total
amount of time he
spent on the phone.
Example 4­5e:
Page 370
Simplify
each
expression. Justify
each steps.
4 ∙ (3c ∙ 2)
Summary: