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.

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

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

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

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

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

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

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

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

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

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

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.

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.

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

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

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

Which property would justify the following statement Associative property of addition Distributive property Addition property of zero Commutative property of addition Answer Now

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

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

Which statement demonstrates the distributive property incorrectly? 3(x + y + z) = 3x + 3y + 3z (a + b) c = ac + bc 5(2 + 3x) = 10 + 3x 6(3k - 4) = 18k - 24 Answer Now

A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2x2

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

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

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.

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

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

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

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

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

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

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

Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ? -36 3a - 36 8a - 36 8a + 36 Answer Now