Reflexive Property of
Equality
Symmetric Property of
Equality
Transitive Property of
Equality
!=!
9.1 = 9.1
If ! = !, then ! = !
9=!
!=9
If ! = ! and ! = !,
then ! = !
27 = ! , ! = 27 and
! = ! then
! = 27
12 = 12
Addition Property of
Equality
If a = b and c = d,
then ! + ! = ! + !
12 + 2.5 = 7
2+5=7
Subtraction Property of
Equality
41 = 41
If a = b and c = d,
then ! − ! = ! − !
48 = 41 + 7
48 = 41 + 7
Multiplication Property
of Equality
If a = b and c = d,
then !" = !"
2
2
2
(27 ÷ 9) = (27) ÷ (9)
3
3
3
Division Property of
Equality
Zero Product Property
Substitution Property
If a = b and c = d
(! ≠ 0 and ! ≠ 0),
then
!
!
=
!
1
4! + 12 = 2! + 12
2
!
If the product of
two factors is zero
If !" = 0 then either
then at least one of
! ≠ 0 or ! ≠ 0
the factors must be
zero.
If ! = !, then ! can
replace ! in any
equation without
changing the value
of the equation
!=2
!+5=7
2+5=7
Commutative Property
of Addition
!+! =!+!
−24 + 35 = 35 + −24
Commutative Property
of Multiplication
!" = !"
45! = !45
!+! +! =!+ !+!
13 + 77 + −4 = 13 + 77 + −4
Associative Property of
Addition
Additive Identity
Property
!+0=!
3
3
− +0=−
5
5
Multiplicative Identity
Property
!∗1=!
34.114 ∗ 1 = 34.114
Distributive Property of
Multiplication Over
Addition
! ! + ! = !" + !"
3! 2! + 7 = 6! ! + 21!
Distributive Property of
Multiplication Over
Subtraction
Quotient Property
! ! − ! = !" − !"
!∗
1 !
=
! !
!≠0
Multiplicative Inverse
1
!∗ =1
!
!≠0
3! ! + 40! ! = ! ! 3! + 40
Suppose John and
Mary are the same
height. Therefore
five less than John’s
height is equal to five
less than Mary’s
height.
1
1=
∗ 17
17
Multiplicative Property
of Zero
!−! =!−!
122 ÷ ℎ = ℎ ÷ 6
The product of any
number and zero
equals zero
0 ∗ 24 = 0
! !" = (!")(!")
120! − 72
= 10! − 6
12
210 + 63! = 21(3! + 10)
6! 2! − 1.5 = 12! − 9.0
When two quantities are
equal, if you add the same
number to both
quantities, the sums will
be equal.
When two quantities
are equal, if you
subtract the same
number to both
quantities, the
differences will be
equal.
When two quantities
are equal, if you
multiply them by the
same number, the
products will be
equal.
When two quantities are
equal, if they are divided
by the same non-zero
number, the quotients will
also be equal.
John and Mary are the
same height. Mary
and Peter are the
same height. John
and Peter are the
same height.
Suppose Fluffy and
Bunny are the same
weight. Therefore,
!"#$$% ÷ 4 = !"##$ ÷ 4