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

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?

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)

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

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

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

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

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