PROPERTIES OF EQUALITY
Quizon, Edelyn Llona
OBJECTIVES
• Identify the Properties of Equality.
• Determine the Properties of Equality
illustrated in the statements.
Properties of Equality
1. Reflexive property of equality
2. Symmetric property of eqality
3. Transitive property of equality
4. Addition property of equality
5. Multiplication property of equality
6. Substitution property of equality
7. Subtraction property of equality
8. Division property of equality
9. Distributive Property of Equality
Reflexive Property of Equality
For any real number a, a=a
EXAMPLES:
1. 3 = 3
2.
1
2
=
1
2
3. -3x = -3x
4. 7y + 1 = 7y + 1
Symmetric Property of Equality
if a = , then b = a
the numbers or expression can be interchanged
EXAMPLES:
1. If x =
5,
2. If -3y =
6,
then 5 =
x.
then 6 = -3y.
3. If 2x + 1 =
-4y,
then -4y = 2x + 1.
Transitive Property of Equality
If a = b, and b = c, then a = c.
A
B
C
EXAMPLES:
1. If 3 + 2 =
5,
and 5 = 4 + 1, then 3 + 2 = 4 + 1
2. If x + 4 = y 7,
and y - 7 = 9, then x + 4 = 9
Addition property of equality
If a = b, then a + c = b + c.
EXAMPLES:
4 = (3 + 2) + __.
4
1. If 5 = 3 +
then 5 + __
9 = 9
2,
-8 = -7 + __.
-8
2. If x + 8 = -7 then (x + 8) + __
x = -15
,
2 = 10 + __.
2
3. If -3y - 2 = 10 then ( -3y - 2) + __
-3y = 12
Multiplication Property of Equality
if a = b, then ac = bc.
EXAMPLES:
then 5( 4 ) = (3 + 3) ( 4 )
1. if 5 = 3 +
20 = 20
3,
1
1
2. if 2x = -6 then 2x ( 2 ) = -6 ( 2 )
x = -3
,
1
1
2. if - y = 6 , then - 4 y ( -4 ) = 6 ( -4 )
4
y = -24
Substitution Property of Equality
if x = y, then y can be substituted for x in any expression
containing x in the equation
EXAMPLES:
1. if x = 3 and y = x + 4
then y = (3) + 4
y = 7
2. if 9x - 5 =
and x = 2
3x + 7
then 9( 2 ) - 5 = 3(2) + 7
18 - 5 = 6 + 7
13 = 13
Subtraction property of equality
if a, b, c are real numbers and , a = b
a - c = b - c
EXAMPLES:
1. if 7 = 20 , then 7 - 4 = 20 - 4
3 = 17
2. if 8 + 2 = 9 + 3
, then (8 + 2) - 2 = (9 + 3) - 2
8 = 10
Division property of equality
𝑎
if a = b, and c is a real number not equal to zero, then: 𝑐 =
EXAMPLES:
1. if 8 = 20 ,
8
20
=
4
4
1. if 6x = 72 then
,
6𝑥
6
=
2 = 5
72
6
𝑥 = 12
𝑎
.
𝑐
Distributive Property of Equality
if a, b, c and are real numbers, then: a ( b + c)
= ab + ac
EXAMPLES:
1. if 3 ( 2 + 5), then 3 ( 2 + 5) = 3 ( 2 ) + 3 ( 5 )
21 = 21
2. if 2 ( 4y + 5y), then 2 ( 4y + 5y) = 2 ( 4y ) + 2 ( 5y )
18y = 18y
EXAMPLE:
1. 2x + 5 = 15
2x = 10
x = 5
if x = 5, then 2 (5)+ 5 = 15
Activity: