Name Class Date 1-5 1 Simplifying Algebraic Expressions Going Deeper Essential question: How do you add, subtract, factor, and multiply algebraic expressions? CC.7.EE.1 EXPLORE Combining Expressions video tutor Jill and Kelly work as consultants and get paid per project. Jill is paid a project fee of $25 plus $10 per hour. Kelly is paid a project fee of $18 plus $14 per hour. Write an expression to represent how much a company will pay to hire both consultants for a project. A Write expressions for how much Jill and Kelly each make per project. Jill: $ $ h Kelly: $ $ h Fee Rate per hour Fee Rate per hour B Add both expressions to represent how much the company will pay to hire both consultants. Let h represent the number of hours they work together. Combine their pay rates. = 25 18 Use the Commutative Property. = h Combine like terms. The company will pay their project. TRY THIS! for both Jill and Kelly to work on 1a. How much do Jill and Kelly make individually if they work 10 hours? 1b. Combine ( 3x 1 2 ) - ( 7x - 4 1 2 ) = ( 3x 1 2 ) [ ( 7x - 4 1 2 ) ] Subtraction is adding the opposite. = ( 3x 1 2 ) ( 7x 4 1 2 ) Distribute the negative sign to each term. = 3x 7x 1 4 1 Use the Commutative Property. 2 2 = Combine like terms. Chapter 1 25 Lesson 5
REFLECT 1c. What are two different ways to calculate how much a company would pay to hire both Jill and Kelly to work on a 10-hour project? 1d. Explain how the Distributive Property allows you to combine the terms 10h and 14h. 2 CC.7.EE.1 EXPLORE Using the Distributive Property Marc is selling tickets for a concert. Adult tickets cost $16.60, and children s tickets cost $12.20. He gets to keep 25% of the money he collects from ticket sales. Write an expression to represent how much Marc gets to keep. A Let a represent the number of adult tickets he sells. Let c represent the number of tickets he sells. B The expression 16.60 12.20 represents the C Write 25% as a decimal. D Write an expression to represent 25% of the money he collects. ( ) 25% of adult ticket and children ticket sales sales E Use the Distributive Property to simplify the expression. 0.25 ( ) 0.25 ( ) = a c TRY THIS! 2. How much does Marc get to keep if he sells 20 adult tickets and 40 children s tickets? Chapter 1 26 Lesson 5
A factor is a number that is being multiplied by another number to get a product. To factor is the process of writing a number or an algebraic expression as a product. 3 CC.7.EE.1 explore Factoring Expressions Factor 4x 8. A Model the expression with algebra tiles. Use positive x tiles and positive one tiles. B Arrange the tiles to form a rectangle. The total area represents 4x 8. C Since the length multiplied by the width equals area, the length and the width of the rectangle are the factors of 4x 8. Find the length and width. The length is x tile and ones tiles or. The width is tiles or. ones D Use the expressions from the length and width of the rectangle to write the area of the rectangle, 4x 8, in factored form. TRY THIS! Factor each expression. 3a. 2x 2 3b. 3x 9 3c. 5x 15 3d. 4x 16 Chapter 1 27 Lesson 5
REFLECT 3e. How could you use the Distributive Property to check your factoring? 3f. What If? How would the model and factors change if the original expression was 4x 8? practice Add or subtract each expression. 1. (4.8x 15.5) (2.1x - 12.2) 2. (7x 8) - (3x 12) 3. ( 1 2 x 3 4 ) ( 1 x - 1 2 4 ) 4. Each week, Joey gets paid $10 plus $2 for each chore he does. His sister Julie gets paid $5 plus $3 per chore. a. Write an expression for how much their parents pay Joey and Julie each week if they do the same amount of chores. b. If Joey and Julie each do 5 chores, how much do they get paid individually? How much do their parents pay altogether? 5. A company sets up a food booth and a game booth at the county fair. The fee for the food booth is $100 plus $5 per day. The fee for the game booth is $50 plus $7 per day. How much does the company pay for both booths for 5 days? 6. A group of 4 people go out to eat. They decide to split the bill so each person pays 1_ of the total price. Appetizers are $6 and main dishes are $9. Write an 4 expression to show how much each person pays. Factor each expression. 7. 24 36x 8. 5x - 25 9. 12x 10 10. 10x - 60 Chapter 1 28 Lesson 5
Name Class Date 1-5 Additional Practice Identify like terms in each list. 1. 3a b 2 b 3 4b 2 4 5a 2. x x 4 4x 4x 2 4x 4 3x 2 3. 6m 6m 2 n 2 2n 2 4m 5n 4. 12s 7s 4 9s s 2 5 5s 4 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 5. 2p 22q 2 p 6. x 2 3x 2 4 2 7. n 4 n 3 3n n n 3 8. 4a 4b 2 2a 5b 1 9. 32m 2 14n 2 12m 2 5n 3 10. 2h 2 3g 2h 2 2 2 3 4g 11. Write an expression for the perimeter of the figure at the right. Then simplify the expression. 12. Write an expression for the combined perimeters of the figures at the right. Then simplify the expression. Chapter 1 29 Practice and Problem Solving
Problem Solving Problem Solving: Simplifying Algebraic Expressions Write the correct answer. Use the figures for Problems 1 3. 1. Figure 1 shows the length of each side of a garden. Write and simplify an expression for the perimeter of the garden. 2. Figure 2 is a square swimming pool. Write and simplify an expression for the perimeter of the pool. 3. Write and simplify an expression for the combined perimeter of the garden and the pool. 4. The Pantheon in Rome has n granite columns in each of 3 rows. Write and simplify an addition expression to show the number of columns. Then evaluate the expression for n 8. Choose the letter for the best answer. 5. Which is an expression that shows the earnings of a telemarketer who worked for 23 hours at a salary of d dollars per hour? A d 23 C d 23 B 23d D 23 d 7. What is the perimeter of a triangle with sides the following lengths: 2a 4c, 3c 7, and 6a 4. Simplify the expression. A 8a 11c B 6a 7c 3 C 8a 7c 3 D 8a 7c 11 6. The minimum wage set in 1997 was $5.15 per hour. Evaluate the expression 40h where h $5.15 to find a worker s weekly salary. F $20.60 H $515.00 G $200 J $206.00 8. A hexagon is a 6-sided figure. Find the perimeter of a hexagon where all of the sides are the same length and the expression x y represents the length of a side. Simplify the expression. F 6x 6y G 6 x y H 6x y J 6xy Chapter 1 30 Practice and Problem Solving