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Bell Ringer 10-11 1-4 Reading Quiz

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. Bell Ringer 10-11 1-4 Reading Quiz .

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Bell Ringer 10-11 1-4 Reading Quiz

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  1. 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 Bell Ringer 10-111-4 Reading Quiz

  2. 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? Review questions in Notebook 10-11

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

  4. 29. Scuba Driving Expression 1: 2($10.95) + 3($7.50) + 2($5.00) + 5(418.99) = $21.90 + $22.50 + $10 + $94.95 $149.35 The total sales are $149.35. Expression 2: 2($10.95 + $5) + 3($7.50) + 5($18.99) 2($15.95) + $22.50 + $94.95 $31.90 + $22.50 + $94.95 $149.35 p. 20 #29

  5. 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. #51

  6. CCSS 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.

  7. Then/Now You explored Associative and Commutative Properties. • Use the Distributive Property to evaluate expressions. • Use the Distributive Property to simplify expressions.

  8. Vocabulary • like terms • simplest form • coefficient

  9. 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. Lesson 1-4 Distributive Property

  10. Concept

  11. Example 1 Distribute Over Addition FITNESSJulio 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. Understand You need to find the total number of minutes Julio walks in a week. Plan Julio walks 5 days for 7 + 2 minutes a day. Solve Write 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.

  12. Example 1 Distribute Over Addition 5(7 + 2) = 5(7)+ 5(2)Distributive Property = 35 + 10 Multiply. = 45 Add. 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.

  13. Example 1 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(15 + 10) using the Distributive Property. Then evaluate to find the total number of minutes Susanne spends walking to and home from school.

  14. Example 2 You can use the distributive property to multiply numbers easier using mental math. Use the Distributive Property to rewrite 6 ● 54. Then evaluate. 6(60 – 6) = 360 – 36 = 324

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

  16. 2. 14(51) = 14(50 + 1) 14(50) + 14(1) 700 + 14 714 So 14(51) = 714 21. 7  497 7(500 – 3) 7(500) – 7(3) 3500 – 21 = 3,479 Distributive Property and Multiplying numbers

  17. 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 5x3 and 4x2 like terms? 25. 2(x + 4) 2x + 8 Distributive property and Simplifying Expressions

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

  19. Example 3 Algebraic Expressions B. Rewrite 4(y2+ 8y + 2) using the Distributive Property. Then simplify. 4(y2 + 8y + 2) = 4(y2) + 4(8y) + 4(2) Distributive Property = 4y2 + 32y + 8 Multiply. Answer: 4y2 + 32y + 8

  20. Example 3 A. Simplify 6(x – 4).

  21. Example 3 B. Simplify 3(x3 + 2x2 – 5x + 7).

  22. Example 4 Combine Like Terms A. Simplify 17a + 21a. 17a + 21a = (17 + 21)a Distributive Property = 38a Substitution Answer: 38a

  23. Example 4 Combine Like Terms B. Simplify 12b2 – 8b2 + 6b. 12b2 – 8b2 + 6b = (12 – 8)b2 + 6b Distributive Property = 4b2 + 6b Substitution Answer: 4b2 + 6b

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

  25. Example 4 D.Simplify 6n2 + 7n + 8n.

  26. Do p. 29 27, 31 – 37odd, 43 and 47 in your notebook 27. (4 – 3m)8 4(8) – 3m(8) 32 – 24m

  27. 31. 7m + 7 – 5m 2m + 7 33. (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

  28. 43. 3m + 5g + 6g + 11m 11g + 14m 47. 2(6x + 4) + 7x 2(6x) + 2(4) + 7x 12x + 8 +7x 19x + 8

  29. Example 5 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)

  30. Example 5 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 – 4y Multiply. = 6x + 20x + 6y – 4y Commutative (+) = 26x + 2ySubstitution Answer: 26x + 2y

  31. Example 5 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. 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)

  32. Example 5 B. Simplify the expression 3(2x – y) + 2(4x + y).

  33. Concept

  34. Additional Examples: -(4x – 6) -1(4x – 6) -1(4x) – 1(-6) -4x + 6 2 ( 15x + 45y + 75) + 8y 3 10x + 30 y + 25 + 8y = 10x + 38y + 25

  35. 4(x + 3) – (5x + 10) 4(x) + 4(3) – 1(5x) – 1(10) 4x + 12 – 5x – 10 -x + 2

  36. p. 29-30 14, 18, 22, 26 – 36 even, 42 – 46 even, 50, 52, 57 Read 1-5 Take Notes Homework 10--11

  37. 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 Exit slip 10-11

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