1. Objective The student will be able to:
recognize and use the properties of identity and equality.

2. Translating verbal expressions into algebraic expressions
Bell Ringer 9/3/14
Translating verbal expressions into algebraic expressions
Which of the following expressions represents 7 times a number decreased by 13?
Which of the following expressions represents six times Bob’s age decreased by 8 ?
Which of the following expressions represents the sum of 5 and a number divided by 3?

3. What do you add to get the same?
Identity Properties
1) Additive Identity
What do you add to get the same?
a + 0 = a
2) Multiplicative Identity
What do you mult. to get the same?
a • 1 = a

4. Inverse Properties 1) Additive Inverse (Opposite) a + (-a) = 0
2) Multiplicative Inverse (Reciprocal)

5. Name the Property
1. 0  12 = 0
Multiplicative Prop. Of Zero
2. (10 + 2)  3 = 12  3
Substitution
= 5 then 5 = 2 + 3
Symmetric

6. 4. If 5  2 = 10 & 10 = then  2 = 5 + 5
Transitive
(-6) = 0
Additive Inverse

7. 6. 1  m = m
Multiplicative Identity
7. k + 7 = k + 7
Reflexive
8. x + 0 = x
Additive Identity 9.
Multiplicative Inverse

8. Name the property. 0 + 4 = 4 Additive Identity Additive Inverse
Additive Property of Zero
Substitution
Answer Now

9. Name the property. 8 – (6 + 2) = 8 - 8
Additive Identity
Additive Inverse
Associative
Substitution
Answer Now

10. Name the property. 2 + (x – 3)1 = 2 + (x – 3)
Reflexive
Multiplicative Inverse
Multiplicative Identity
Symmetric
Answer Now

11. Objective The student will be able to:
recognize and use the commutative and associative properties and the properties of equality.

12. Commutative Property
Commutative means that the order does not make any difference.
a + b = b + a a • b = b • a
Examples
4 + 5 = 5 + 4
2 • 3 = 3 • 2
The commutative property does not work for subtraction or division.

13. Associative Property
Associative means that the grouping does not make any difference.
(a + b) + c = a + (b + c) (ab) c = a (bc)
Examples
(1 + 2) + 3 = 1 + (2 + 3)
(2 • 3) • 4 = 2 • (3 • 4)
The associative property does not work for subtraction or division.

14. Name the property 1) 5a + (6 + 2a) = 5a + (2a + 6)
commutative (switching order)
2) 5a + (2a + 6) = (5a + 2a) + 6
associative (switching groups)
3) 2(3 + a) = 6 + 2a
distributive

15. Which property would justify rewriting the following expression without parentheses? 3(2x + 5y)
Associative property of multiplication
Distributive property
Addition property of zero
Commutative property of multiplication

16. Which property would justify the following statement? 8x + 4 = 4 + 8x
Associative property of addition
Distributive property
Addition property of zero
Commutative property of addition

17. Which property would justify the following statement
Associative property of addition
Distributive property
Addition property of zero
Commutative property of addition