Transcript Properties of Mathematics Pamphlet

Properties of
Mathematics Pamphlet
Pre-Algebra
2 December 2008
Name of the Property
In
symbols
Examples
In words:
Multiplicative Property of Zero
In words:
Any number
multiplied
by zero is
zero.
Multiplicative Property of Zero
a0  0
Examples
50  0
256  0  0
 46  0  0
In words:
Any number
multiplied
by zero is
zero.
Identity Property of
Multiplication
In words:
Any number
multiplied
by one is
equal to
itself.
Identity Property of
Multiplication
a 1  a
Examples
5 1  5
256 1  256
 46 1  46
In words:
Any number
multiplied
by one is
equal to
itself.
Identity Property of Addition
In words:
Any number
plus zero is
equal to
itself.
Identity Property of Addition
a0  a
Examples
50  5
256  0  256
 46  0  46
In words:
Any number
plus zero is
equal to
itself.
Commutative Property of
Addition
In words: If
you change
the order of
the numbers
you are
adding, the
answer is the
same.
Commutative Property of
Addition
In words: If
a b  b a
Examples
56  65
224  5  5  224
( 46)  1  1  (46)
you change
the order of
the numbers
you are
adding, the
answer is the
same.
Commutative Property of
Multiplication
In words: If
you change
the order of
the numbers
you are
multiplying,
the answer is
the same.
Commutative Property of
Multiplication
ab  ba
Examples
56  65
224  5  5  224
(46) 1  1  (46)
In words: If
you change
the order of
the numbers
you are
multiplying,
the answer is
the same.
Associative Property of Addition
In words: If
you change
the location
of the
parenthesis
in an addition
problem, the
answer is the
same.
Associative Property of Addition
In words: If
(a  b)  c  a  (b  c)
Examples
(5  6)  7  5  (6  7)
(a  3)  5  a  (3  5)
2  (1  6  3)  (2  1  6)  3
you change
the location
of the
parenthesis
in an addition
problem, the
answer is the
same.
Associative Property of
Multiplication
 In words: If
you change the
location of the
parenthesis in
a multiplication
problem, the
answer is the
same.
Associative Property of
Multiplication
(ab)c  a (bc )
Examples
(5  6)  7  5  (6  7)
(a  3)  5  a (3  5)
2(1  6  3)  (2 1  6)  3
 In words: If
you change the
location of the
parenthesis in
a multiplication
problem, the
answer is the
same.
Test Yourself
 Which property is demonstrated by the following
statement?
5 4  45
Test Yourself
 Which property is demonstrated by the following
statement?
0  10  10
Test Yourself
 Which property is demonstrated by the following
statement?
2,451  0  0
Test Yourself
 Which property is demonstrated by the following
statement?
(1  b)  7  1  (b  7)
Test Yourself
 Which property is demonstrated by the following
statement?
(1 4)  7  1 (4  7)
Test Yourself
 Which property is demonstrated by the following
statement?
8 w  w8
Test Yourself
 Which property is demonstrated by the following
statement?
k 0  0