1. What is the Title of Lesson 1-4? 2. What is the Distributive Property? 3. What are 2 ways that...

BELL RINGER 10-111-4 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

REVIEW QUESTIONS IN NOTEBOOK 10-11

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?

P. 20 #29 29. Scuba DrivingExpression 1: 2($10.95) + 3($7.50) + 2($5.00) +

5(418.99) = $21.90 + $22.50 + $10 + $94.95

$149.35The 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

#51 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.

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.

THEN/NOW

You explored Associative and Commutative Properties.

• Use the Distributive Property to evaluate expressions.

• Use the Distributive Property to simplify expressions.

VOCABULARY

• like terms

• simplest form

• coefficient

LESSON 1-4 DISTRIBUTIVE PROPERTY

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.

CONCEPT

EXAMPLE 1 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.

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 theproduct of the number of days that Julio walks and the sum of the

number of minutes he walks at each rate.

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.

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.

EXAMPLE 2

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.

DISTRIBUTIVE PROPERTY AND MULTIPLYING NUMBERS

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

2. 14(51) = 14(50 + 1)

14(50) + 14(1) 700 + 14

714So 14(51) = 71421. 7 497 7(500 – 3) 7(500) – 7(3) 3500 – 21 = 3,479

DISTRIBUTIVE PROPERTY AND SIMPLIFYING EXPRESSIONS

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

EXAMPLE 3Algebraic 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

EXAMPLE 3Algebraic 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

EXAMPLE 3

A. Simplify 6(x – 4).

EXAMPLE 3

B. Simplify 3(x3 + 2x2 – 5x + 7).

EXAMPLE 4Combine Like Terms

A. Simplify 17a + 21a.

17a + 21a = (17 + 21)a Distributive Property

= 38a Substitution

Answer: 38a

EXAMPLE 4Combine Like Terms

B. Simplify 12b2 – 8b2 + 6b.

12b2 – 8b2 + 6b = (12 – 8)b2 + 6b Distributive

Property

= 4b2 + 6bSubstitution

Answer: 4b2 + 6b

Example: C. -3(3m + 5m)

-3(3m) - 3(5m) -9m - 15m like terms

-24m

EXAMPLE 4

D. Simplify 6n2 + 7n + 8n.

Do p. 29 27, 31 – 37odd, 43 and 47 in your notebook

27. (4 – 3m)8 4(8) – 3m(8) 32 – 24m

31. 7m + 7 – 5m 2m + 7

33. (2 – 4n)17 2(17) – 4n (17) 34 – 68n

35. 7m + 2m + 5p + 4m13m + 5p

37. 4(fg + 3g) + 5g 4fg + 12g + 5g

4fg + 17g

43. 3m + 5g + 6g + 11m11g + 14m

47. 2(6x + 4) + 7x2(6x) + 2(4) + 7x12x + 8 +7x

19x + 8

EXAMPLE 5Write 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)

EXAMPLE 5Write 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 + 2y Substitution

Answer: 26x + 2y

EXAMPLE 5

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.

EXAMPLE 5

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

CONCEPT

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

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

HOMEWORK 10--11

p. 29-30 14, 18, 22, 26 – 36 even, 42 – 46 even, 50, 52, 57

Read 1-5 Take Notes

EXIT SLIP 10-11

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