Transcript Properties of Equality, Identity, and Operations

Properties of Equality, Identity,
and Operations
Commutative Property
a+b=b+a
(a)(b) = (b)(a)
• The Commutative Property states that the order
of the numbers may change and the
sum/product will remain the same.
• This property applies to both addition and
multiplication.
2+3=3+2
(2)(3) = (3)(2)
Associative Property
(a + b) + c = a + (b + c)
(a · b) · c = a · (b · c)
• The Associative Property states that the
grouping of numbers can change and the
sum/product will remain the same.
• This property applies to both addition and
multiplication.
(2 + 4) + 5 = 2 + (4 + 5)
(2 · 4) · 5 = 2 · (4 · 5)
Distributive Property of Multiplication
a (b + c) = a(b) + a(c)
a (b – c) = a(b) – a(c)
• The Distributive Property takes a number and
multiplies it by everything inside the
parentheses.
• This property works over addition and
subtraction.
2(3 + 4) = 2(3) + 2(4)
2 (5 – 2) = 2(5) – 2(2)
Substitution Property
Solve: y = 2(x) + 4
if x = 5
• This property allows you to simplify algebraic
expressions for different values. You substitute
the given value of the variable into the equation
and solve.
y = 2(5) + 4
y = 10 + 4
y = 14
Identity Properties
n·1=n
n+0=n
• This property shows how a given number is itself
when multiplied by 1 or added to 0.
• These are important concepts to understand
when solving single and multi-step equations.
• The one and zero act like mirrors.
4·1=4
5+0=5
Zero Property of Multiplication
n·0=0
Simply stated, any number times zero
equals zero.
Multiplicative Inverse Property
½ (2) = 1
• This property is helpful when solving equations
where there is a fraction “attached” to a variable
by multiplication. The normal inverse operation
for multiplication is division, but in this case, you
will multiply both sides of the equation by the
reciprocal of the fraction.
½n–3=4
½ n -3 + 3 = 4 + 3
½n=7
½ n (2) = 7(2)
n = 14
Transitive Property
If a = b and b = c, then a = c
If one quantity equals a second quantity and the
second quantity equals a third quantity, then the
first equals the third.
If 1000 mm = 100 cm and 100 cm = 1 m,
Then 1000 mm = 1m
Symmetric Property
If a + b = c then c = a + b
If one quantity equals a second quantity, then
the second quantity equals the first.
If 10 = 4 + 6, then 4 + 6 = 10
Reflexive Property
a=a
a+b=a+b
Any quantity is equal to itself.
7=7
2+3=2+3