Commutative Properties are the properties
that allows us to change the order of addition
and multiplication statements.
ORDER DOES NOT MATTER!
It does not work for subtraction or division.
Commutative of Addition: a + b = b + a
3+8=8+3
Commutative of multiplication: a•b = b•a
3•8 = 8•3
Associative Properties are the properties
that allows us to change the grouping of an
addition or multiplication statement without
changing its value.
It does not work with division or
subtraction.
Associative of addition:
(a + b) + c = a+ (b+c)
(6 + 4) + 5 = 6 + (4+5)
Associative of multiplication:
(a•b)•c = a•(b•c)
(6•4)•5 = 6•(4•5)
Distributative Property is the property that
allow us to rewrite statements that involve
parentheses.
a(b+c) = ab + ac
5(4+2) = 5•4 + 5•2
3(n+5) = 3n + 3•5
4(9-2) = 4•9 - 4•2
4(n-3) = 4n - 4•3
3(4n + 12) = 3•4n + 3• 12
Identity properties are the properties that
allows us to do an operation on a value, but
still maintain the same value.
Identity property of addition:
a + 0 =a and 6 + 0 =6
Identity property of multiplication:
a•1 = a and 6•1 = 6
Inverse Properties are the properties that
allow us to solve algebraic equations while
keeping the equations balanced.
Inverse property of addition:
Add opposites to equal 0.
5 + (-5) = 0
- 7/8 + 7/8 =0
-7 + 7 =0
a + -a = 0
Inverse property of multiplication:
Multiply by the reciprocal to equal 1.
a • 1/a = 1
1/3 • 3/1 =1
5 • 1/5 =1
6/7 • 7/6 = 1
The zero property is the product of any
number or value equals 0.
5•0=0
a • 0 =0