Splash Screen. Lesson Menu Five-Minute Check (over Lesson 1–3) Then/Now New Vocabulary Key Concept: Distributive Property Example 1: Real-World: Distribute.

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1-4: The Distributive Property

Algebra 1 Notes: Lesson 1-6: Commutative and Associative Properties

Properties of Numbers Use mental math to simplify –2 • 13 • 5.

Objectives Use the Commutative, Associative, and Distributive Properties to simplify expressions.

Which property is demonstrated in the equation 8 • 0 = 0?

Objectives Use the Commutative, Associative, and Distributive Properties to simplify expressions.

The Distributive Property

Presentation transcript:

Splash Screen

Lesson Menu Five-Minute Check (over Lesson 1–3) Then/Now New Vocabulary Key Concept: Distributive Property Example 1: Real-World: Distribute Over Addition Example 2:Mental Math Example 3:Algebraic Expressions Example 4:Combine Like Terms Example 5:Write and Simplify Expressions Concept Summary: Properties of Numbers

Then/Now You explored Associative and Commutative Properties. (Lesson 1-3) Use the Distributive Property to evaluate expressions. Use the Distributive Property to simplify expressions.

Vocabulary like terms simplest form coefficient

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. UnderstandYou need to find the total number of minutes Julio walks. PlanJulio walks for or 9 minutes a day. SolveWrite an expression that shows the product of the minutes Julio walks for 5 days.

Example 1 Distribute Over Addition 5(7 + 2)=5(7) + 5(2)Distributive Property = Multiply. =45Add. Answer: Julio walks 45 minutes a week. Check: Use estimation to check your answer. 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.

[Enter question here] A.(15 + 5) ● 10; 65 minutes B.(5 ● 15) + 10; 85 minutes C.(5 ● 15) + (5 ● 10); 125 minutes D ; 25 minutes 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.

Example 2 Mental Math Use the Distributive Property to find 12 ● 82. Then evaluate. 12 ● 82=12(80 + 2)Think: 82 = =12(80) + 12(2)Distributive Property = Multiply. =984 Add. Answer: 984

[Enter question here] Use the Distributive Property to find 6 ● 54.

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

Example 3 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 + 8Multiply. Answer: 4y y + 8

[Enter question here] A.6x – 4 B.6x – 24 C.x – 24 D.6x + 2 A. Simplify 6(x – 4).

[Enter question here] A.3x 3 + 2x 2 – 5x + 7 B.4x 3 + 5x 2 – 2x + 10 C.3x 3 + 6x 2 – 15x + 21 D.x 3 + 2x 2 –5x +21 B. Simplify 3(x 3 + 2x 2 – 5x + 7).

Example 4 Combine Like Terms A. Simplify 17a + 21a. 17a + 21a = ( )aDistributive Property = 38aSubstitution Answer: 38a

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

[Enter question here] A.5x 2 B.23x C.5 D.5x A. Simplify 14x – 9x.

[Enter question here] A.6n n B.21n 2 C.6n n D.62n 2 B. Simplify 6n 2 + 7n + 8n.

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)

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

[Enter question here] 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.

[Enter question here] A.2x + 4y B.11x C.14x – y D.12x + y B. Simplify the expression 3(2x – y) + 2(4x + y).

Concept

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