 1. What is the Title of Lesson 1-4?  2. What is the Distributive Property?  3. What are 2 ways that the Distributive property can be used?  4. What is a term?  5. When is an expression written in simplest form? Keep your Homework -Review/Questions

1. What is the difference between the multiplicative inverse and additive inverse? 2. Does the commutative property always, sometimes or never hold for subtraction? Explain your reasoning. 3. What is the difference between the commutative and reflexive property?

4. What is the school’s focus the next few weeks?

 29. Scuba Driving Expression 1: 2($10.95) + 3($7.50) + 2($5.00) + 5(418.99) = $ $ $10 + $94.95 $ The total sales are $ Expression 2: 2($ $5) + 3($7.50) + 5($18.99) 2($15.95) + $ $94.95 $ $ $94.95 $149.35

 51. Geometry: A regular octagon measures (3x + 5) units on each side. What is the perimeter if x = 2? Each side is 3x + 5 units. 3(2) + 5 = 11 So each side of the octagon is 11 units. How do you find the perimeter of a shape? Add all the sides. How many sides does an octagon have? (11)(8) = 88 So the perimeter is 88 units.

Content Standards A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients. A.SSE.2 Use the structure of an expression to identify ways to rewrite it. Mathematical Practices 1 Make sense of problems and persevere in solving them. 8 Look for and express regularity in repeated reasoning.

You explored Associative and Commutative Properties. Use the Distributive Property to evaluate expressions. Use the Distributive Property to simplify expressions.

like terms simplest form coefficient

 Objectives: By the end of class, students will be able to:  Use the distributive property to evaluate and simplify expressions. with 90% or above mastery.

Distribute Over Addition FITNESS Julio walks 5 days a week. He walks at a fast rate for 7 minutes and cools down for 2 minutes. Use the Distributive Property to write and evaluate an expression that determines the total number of minutes Julio walks. UnderstandYou need to find the total number of minutes Julio walks in a week. PlanJulio walks 5 days for minutes a day. SolveWrite an expression that shows the product of the number of days that Julio walks and the sum of the number of minutes he walks at each rate.

Distribute Over Addition 5(7 + 2)=5(7) + 5(2)Distributive Property = Multiply. =45Add. Answer: Julio walks 45 minutes a week. Check: The total number of days he walks is 5 days, and he walks 9 minutes per day. Multiply 5 by 9 to get 45. Therefore, he walks 45 minutes per week.

WALKING Susanne walks to school and home from school 5 days each week. She walks to school in 15 minutes and then walks home in 10 minutes. Rewrite 5( ) using the Distributive Property. Then evaluate to find the total number of minutes Susanne spends walking to and home from school.

Use the Distributive Property to rewrite 6 ● 54. Then evaluate. 6(60 – 6) = 360 – 36 = 324 You can use the distributive property to multiply numbers easier using mental math.

Next example 7(49) = 7(50 – 1) 7(50) + 7(-1) 350 – 7 = 343 Do p. 29 #2 and 21

2. 14(51) = 14(50 + 1) 14(50) + 14(1) So 14(51) =  497 7(500 – 3) 7(500) – 7(3) 3500 – 21 = 3,479

 You can also use the distributive property to simplify expressions.  When is an expression in simplest form?  An expression is in simplest form when it has no like terms or parentheses.  A term is a number, variable or a product of a number and a variable.  What are like terms?  Like terms have the same variable and power. See p. 27. Are 5x 3 and 4x 2 like terms? 25. 2(x + 4) 2x + 8

Algebraic Expressions A. Rewrite 12(y + 3) using the Distributive Property. Then simplify. 12(y + 3)=12 ● y + 12 ● 3 Distributive Property =12y + 36Multiply. Answer: 12y + 36

Algebraic Expressions B. Rewrite 4(y 2 + 8y + 2) using the Distributive Property. Then simplify. 4(y 2 + 8y + 2) = 4(y 2 ) + 4(8y) + 4(2) Distributive Property = 4y y + 8 Multiply. Answer: 4y y + 8

A. Simplify 6(x – 4).

B. Simplify 3(x 3 + 2x 2 – 5x + 7).

Combine Like Terms A. Simplify 17a + 21a. 17a + 21a = ( )aDistributive Property = 38aSubstitution Answer: 38a

Combine Like Terms B. Simplify 12b 2 – 8b 2 + 6b. 12b 2 – 8b 2 + 6b = (12 – 8)b 2 + 6b Distributive Property = 4b 2 + 6bSubstitution Answer: 4b 2 + 6b

Example: C. -3(3m + 5m) -3(3m) - 3(5m) -9m - 15m like terms -24m

D. Simplify 6n 2 + 7n + 8n.

Do p , 31 – 37odd, 43 and 47 in your notebook 27. (4 – 3m)8 4(8) – 3m(8) 32 – 24m

31. 7m + 7 – 5m 2m (2 – 4n)17 2(17) – 4n (17) 34 – 68n 35. 7m + 2m + 5p + 4m 13m + 5p 37. 4(fg + 3g) + 5g 4fg + 12g + 5g 4fg + 17g

43. 3m + 5g + 6g + 11m 11g + 14m 47. 2(6x + 4) + 7x 2(6x) + 2(4) + 7x 12x x 19x + 8

Write and Simplify Expressions Use the expression six times the sum of x and y increased by four times the difference of 5x and y. A. Write an algebraic expression for the verbal expression. Answer: 6(x + y) + 4(5x – y)

Write and Simplify Expressions B. Simplify the expression and indicate the properties used. 6(x + y) + 4(5x – y) = 6(x) + 6(y) + 4(5x) – 4(y) Distributive Property = 6x + 6y + 20x – 4yMultiply. = 6x + 20x + 6y – 4yCommutative (+) = 26x + 2ySubstitution Answer: 26x + 2y

A.3(2x + y) + 2(4x – y) B.3(2x – y) + 2(4x + y) C.2(2x – y) + 3(4x + y) D.3(x – 2y) + 2(4x + y) Use the expression three times the difference of 2x and y increased by two times the sum of 4x and y. A. Write an algebraic expression for the verbal expression.

B. Simplify the expression 3(2x – y) + 2(4x + y).

Additional Examples: -(4x – 6) -1(4x – 6) -1(4x) – 1(-6) -4x ( 15x + 45y + 75) + 8y 3 10x + 30 y y = 10x + 38y + 25

4(x + 3) – (5x + 10) 4(x) + 4(3) – 1(5x) – 1(10) 4x + 12 – 5x – 10 -x + 2

p , 18, 22, 26 – 36 even, 42 – 46 even, 50, 52, 57 Read 1-5 Take Notes

 1. What is the distributive property?  2. What are like terms?  3. Use the distributive property to simplify 3(2x + 6). 4. Simplify 6(x – 9) + 15x