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**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.

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**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

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**Inverse Properties 1) Additive Inverse (Opposite) a + (-a) = 0**

2) Multiplicative Inverse (Reciprocal)

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**Multiplicative Property of Zero**

(If you multiply by 0, the answer is 0.)

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**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

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

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

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

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**Name the property. 0 + 4 = 4 Additive Identity Additive Inverse**

Additive Property of Zero Substitution Answer Now

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**Name the property. 8 – (6 + 2) = 8 - 8**

Additive Identity Additive Inverse Associative Substitution Answer Now

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**Name the property. 2 + (x – 3)1 = 2 + (x – 3)**

Reflexive Multiplicative Inverse Multiplicative Identity Symmetric Answer Now

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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.

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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.

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**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

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**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 Answer Now

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**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 Answer Now

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**Which property would justify the following statement**

Associative property of addition Distributive property Addition property of zero Commutative property of addition Answer Now

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**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

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

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**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 Answer Now

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**A term is a 1) number, 2) variable, or**

3) a product / quotient of numbers and variables. Example 5 m 2x2

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**the numerical part of the term.**

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

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**Like Terms are terms with the same variable AND exponent.**

To simplify expressions with like terms, simply combine the like terms.

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**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.

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**Which of the following is the simplified form of -4x + 7x ?**

Answer Now

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5a and a are like terms and are like terms The above expression simplifies to:

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**Simplify 1) 5a + 7a 12a 2) 6.1y - 3.2y 2.9y 3) 4x2y + x2y 5x2y**

4) 3m2n + 10mn2 + 7m2n - 4mn2 10m2n + 6mn2

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

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**Which of the following is the simplified form of 5x - 4 - 7x + 14 ?**

Answer Now

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**If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle?**

Answer Now

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**Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles?**

Answer Now

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**Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ?**

-36 3a - 36 8a - 36 8a + 36 Answer Now

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