Transcript Properties

Properties of Addition &
Multiplication
Commutative Property
• Switching the order when
adding or multiplying does not
change the answer (#’s move)
• Switching the order may help you
to solve the problem.
• 3 + 4 = 4 + 3 or 6 x 8 = 8 x 6
• 95 + 32 + 5 = 95 + 5 + 32
Associative Property
Moving the grouping symbols
(parentheses) does not affect the
answer.
2+(4 + 5) = (2 + 4)+5
2+9
11
= 6 + 5
=
11
(3x5)x 6=3x(5x6)
15 x 6 = 3 x 30
90 = 90
Identity Properties
Identity Property of
Addition
• A number keeps its “identity”
when zero is added to it.
25 + 0 = 25
(5 + 6) + 0 = (5 + 6)
2a + 0 = 2a
Identity Property of
Multiplication
• A number keeps its “identity”
when multiplied by 1.
25 x 1 = 25
(5 +6) x 1 = (5 + 6)
2a x 1 = 2a
Multiplicative Property
of Zero
Multiplicative Property
of Zero
When any number is
multiplied by 0, the
result is 0.
2543 x 0 = 0
(5 + 4m) x 0 = 0
Distributive Property
Distributive Property
A number multiplied by a quantity
in parentheses can be rewritten
without the parentheses. This will
not affect the result.
1.
7 (6 – 3) = (7 x 6) – (7 x 3)
7 x 3 = 42 – 21
21 = 21
Distributive Property
A number multiplied by a quantity
in parentheses can be rewritten
without the parentheses. This will
not affect the result.
2. 4(5 + m) = (4 x 5) + (4 x m)
= 20 + 4m
Inverse Properties
Inverse Properties
Numbers that combine with
other numbers to result in
identity elements. So,
inverse for addition would
equal 0 and inverse for
multiplication would
equal 1.
Inverse Properties
Addition
(remember opposites)
5 + (-5) = 0
13 + (-13) = 0
5x + (-5x) = 0
Inverse Properties
Multiplication
(remember flip it)
5 x 1/5 = 1
5/7 x 7/5 = 1
½x2=1
EXAMPLES
• (9 + 5) + 2 = 9 + (5 +2)
•4X3X2=2X3X4
• 54 X 0 = 0
• 456 + 5 = 5 + 456
EXAMPLES
• 79 + 0 = 79
• 3(34 + 8) = 3 X 34 + 3 X 8
• 67 X 1 = 67
•¼X4=1