1. 3.1.1: Properties of Equality/Operations
(8/29/2018)
When we solve an equation, we are rewriting it into a simpler, equivalent equation that helps us find the unknown value.
Properties of Equality, and Properties of Operations, justify our reasoning, and also help us to understand our own thinking.
When operations are performed on one side of the equation, the Properties of Operations are generally followed.
When an operation is performed on both sides of the equation, the Properties of Equality are generally followed.(Balance the equation)
3.1.1: Properties of Equality

2. Key Concepts, continued Properties of Equality
Property
Symbolically
In words
Reflexive property
of equality(Same)
a = a
A number is equal to itself.
Symmetric property
of equality(Switch)
If a = b, then b = a.
If numbers are equal, they will still be equal if the order is changed.
Transitive property
of equality(Three)
If a = b and b = c, then a = c.
If numbers are equal to the same number, then they are equal to each other.
Addition property
of equality
If a = b, then a + c = b + c.
Adding the same number to both sides of an equation does not change the equality of the equation.
3.1.1: Properties of Equality

3. Key Concepts, continued Properties of Equality, continued
Property
Symbolically
In words
Subtraction
property of equality
If a = b, then
a – c = b – c.
Subtracting the same number from both sides of an equation does not change the equality of the equation.
Multiplication
If a = b and
c ≠ 0, then
a • c = b • c.
Multiplying both sides of the equation by the same number, other than 0, does not change the equality of the equation.
Division property
of equality
a ÷ c = b ÷c.
Dividing both sides of the equation by
the same number, other than 0, does not change the equality of the equation.
3.1.1: Properties of Equality

4. Key Concepts, continued Properties of Equality, continued
Property
Symbolically
In words
Substitution
If a = b, then b may be
substituted for a in any
expression containing a.
If two numbers are equal, then
substituting one in for another does not change the equality of the equation.
3.1.1: Properties of Equality

5. Key Concepts, continued
Properties of Operations: explain the effect that the operations of addition, subtraction, multiplication, and division have on equations.
Property
General rule
Specific example
Commutative property of addition
a + b = b + a
3 + 8 = 8 + 3
Associative property of addition
(a + b) + c = a + (b + c)
(3 + 8) + 2 = 3 + (8 + 2)
Commutative property of
multiplication
a • b = b • a
3 • 8 = 8 • 3
Associative property of
(a • b) • c = a • (b • c)
(3 • 8) • 2 = 3 • (8 • 2)
Distributive property of
multiplication over addition
a • (b + c) = a • b + a • c
3 • (8 + 2) = 3 • • 2
3.1.1: Properties of Equality

6. Common Errors/Misconceptions
incorrectly identifying operations
incorrectly identifying properties
performing a step that is not justifiable or does not follow the properties of equality and/or the properties of operations
3.1.1: Properties of Equality

7. Guided Practice Example #1, P.9:
Which property of equality is missing in the steps to solve the equation –7x + 22 = 50?
Equation
Steps
1) –7x + 22 = 50
1) Original equation(Given)
2) –7x = 28
3) x = –4
3) Division property of equality
2) Subtraction Property of Equality
3.1.1: Properties of Equality

8. Guided Practice Example #2, P.10
Which property of equality is missing in the steps to
solve the equation ?
Equation
Steps
1) Original equation(Given)
2) Addition property of equality
3) –x = 42
4) x = –42
4) Division property of equality
3) Multiplication Property of Equality
3.1.1: Properties of Equality

9. Guided Practice Example #3, P.10:
Which property of equality is missing in the steps to
solve the equation 76 = 5x – x ?
Equation
Steps
1) 76 = 5x – x
1) Original Equation(Given)
2) 76 = 5x + 2x - 15
2) Commutative Property of Addition
3) 76 = 7x - 15
3) Combine Like Terms(Simplify)
4) 91 = 7x
4) Addition Property of Equality
5) 13 = x
5) Division Property of Equality
6) x = 13
6) Symmetric Property of Equality
3.1.1: Properties of Equality

10. Guided Practice Example #4, P.10:
Which property of equality is missing in the steps to
solve the equation 5x + 3(x + 4) = 28 ?
Equation
Steps
1) 5x + 3(x+4) = 28
1) Original Equation(Given)
2) 5x + 3x + 12 = 28
2) Distributive Property
3) 8x + 12 = 28
3) Combine Like Terms(Simplify)
4) 8x = 16
4) Subtraction Property of Equality
5) x = 2
5) Division Property of Equality
3.1.1: Properties of Equality

11. 8/29/2018: Classwork Workbook(3.1.1): P.13,14 #1-8 5 minutes!!!!!

12. 3.1.1, P.13/14 #1-8 Equation Steps #1- 2) Add P of E #2- 2) Div P of E
#5- 3) 2x = 2.6
#5- 4) Div P of E
#6- 4) x = - 4
#6- 3) Subt P of E
#7- 2) Div P of E
#7- 3) Add P of E
Common Core State Standard: A–REI.3
#8- 2) CLT (Simplify)
#8- 3) Subt P of E
#8- 4) Div P of E
3.1.2: Solving Linear Equations

13. 8/29/2018: 2) 3.1.2 Notes(U3-11) Homework
Finish Algebra Proof worksheet
2) Notes(U3-11)
a) Intro: read only
b) Key Concepts: copy the 1 Chart(U3-11)
c) Workbook: P.19, Example #1

14. 3.1.1 Handout, #5(On back of handout)
Equation
Steps
1) 3x - 4 = 7x -11
1) Given
2) -4x - 4 = -11
2) Subtraction Property of Equality(P of E)
3) -4x = -7
3) Addition P of E
4) Division P of E OR
Equation
Steps
1) 3x - 4 = 7x -11
1) Given
2) -4x - 4 = -11
2) Subtraction Property of Equality(P of E)
3) -4x = -7
3) Addition P of E
4) Division P of E
3.1.1: Properties of Equality