1. Lesson 1 Algebraic Properties of Equality and Identity
NCSCOS Obj.: 1.01, 1.02
Objective TLW recognize and use the properties of identity and equality.

2. 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

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

4. Multiplicative Property of Zero
(If you multiply by 0, the answer is 0.)

5. Properties of Equality
1) Reflexive: a = a
5 = 5
2) Symmetric: If a = b then b = a.
If 4 = then = 4.
3) Transitive:If a = b and b = c, then a = c.
If 4 = and = then 4 =
4) Substitution: If a = b, then a can be replaced by b.
(5 + 2)x = 7x

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

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

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

9. Name the property. 0 + 4 = 4 Additive Identity Additive Inverse
Additive Property of Zero
Substitution
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10. Name the property. 8 – (6 + 2) = 8 - 8
Additive Identity
Additive Inverse
Associative
Substitution
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11. Name the property. 2 + (x – 3)1 = 2 + (x – 3)
Reflexive
Multiplicative Inverse
Multiplicative Identity
Symmetric
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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
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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
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17. Which property would justify the following statement
Associative property of addition
Distributive property
Addition property of zero
Commutative property of addition
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18. The Distributive Property
The process of distributing the number on the outside of the parentheses to each term on the inside.
a(b + c) = ab + ac and (b + c) a = ba + ca
a(b - c) = ab - ac and (b - c) a = ba - ca
Example #1
5(x + 7)
5 • x + 5 • 7
5x + 35

19. Example #2
3(m - 4)
3 • m - 3 • 4
3m - 12
Example #3
-2(y + 3)
-2 • y + (-2) • 3
-2y + (-6)
-2y - 6

20. Which statement demonstrates the distributive property incorrectly?
3(x + y + z) = 3x + 3y + 3z
(a + b) c = ac + bc
5(2 + 3x) = x
6(3k - 4) = 18k - 24
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21. A term is a 1) number, 2) variable, or
3) a product / quotient of numbers and variables.
Example 5 m
2x2

22. the numerical part of the term.
The coefficient is
the numerical part of the term.
Examples
1) 4a 4
2) y2 1 3)

23. Like Terms are terms with the same variable AND exponent.
To simplify expressions with like terms, simply combine the like terms.

24. Are these like terms? 1) 13k, 22k Yes, the variables are the same.
2) 5ab, 4ba
Yes, the order of the variables doesn’t matter.
3) x3y, xy3
No, the exponents are on different variables.

25. Which of the following is the simplified form of -4x + 7x ?
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26. 5a and a are like terms
and
are like terms
The above expression simplifies to:

27. Simplify 1) 5a + 7a 12a 2) 6.1y - 3.2y 2.9y 3) 4x2y + x2y 5x2y
4) 3m2n + 10mn2 + 7m2n - 4mn2
10m2n + 6mn2

28. 5) 13a + 8a + 6b
21a + 6b
6) 4d + 6a2 - d + 12a2
18a2 + 3d 7) y

29. Which of the following is the simplified form of 5x - 4 - 7x + 14 ?
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30. If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle?
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31. Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles?
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32. Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ?
-36
3a - 36
8a - 36
8a + 36
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