Lesson 7.5. Week Value of w Amount Saved = 25 + _ = = 25 + _ = = 25 + _ =
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1 Name Evaluate Algebraic Expressions and Formulas Essential Question How do you evaluate an algebraic expression or a formula? To evaluate an algebraic expression, substitute numbers for the variables and then follow the order of operations. Lesson 7.5 Expressions and Equations 6.EE.A.2c MATHEMATICAL PRACTICES MP4, MP5, MP6 Unlock the Problem Amir is saving money to buy an MP3 player that costs $120. He starts with $25, and each week he saves $9. The expression w gives the amount in dollars that Amir will have saved after w weeks. A How much will Amir have saved after 8 weeks? Which operations does the expression w include? In what order should you perform the operations? Evaluate the expression for w = 8. Substitute 8 for w. Multiply. Add w So, Amir will have saved $ after 8 weeks. Image Credits: (r) Stock4B/Getty Images B After how many weeks will Amir have saved enough money to buy the MP3 player? Make a table to find the week when the amount saved is at least $120. Week Value of w Amount Saved = 25 + = = 25 + = = 25 + = So, Amir will have saved enough money for the MP3 player after weeks. Math Talk MATHEMATICAL PRACTICES 6 Explain What does it mean to substitute a value for a variable? Chapter 7 381
2 Example 1 A 4 (m 8) 3 for m = 14 Evaluate the expression for the given value of the variable. Substitute 14 for m. Perform operations in parentheses. Multiply and divide from left to right. 4 (m 8) 3 4 ( 8) B 3 ( y 2 + 2) for y = 4 3 ( y 2 + 2) Substitute 4 for y. Follow the order of operations within the parentheses. Multiply. 3 ( 2 + 2) 3 ( + 2) 3 When squaring a number, be sure to multiply the number by itself. 4 2 = 4 4 Recall that a formula is a set of symbols that expresses a mathematical rule. Example 2 The formula P = 2l 2w gives the perimeter P of a rectangle with length l and width w. What is the perimeter of a rectangular garden with a length of 2.4 meters and a width of 1.2 meters? Write the expression for the perimeter of a rectangle. 2l + 2w Substitute 2.4 for l and for w Multiply from left to right. Add. So, the perimeter of the garden is meters Math Talk MATHEMATICAL PRACTICES 61 Compare How is evaluating an algebraic expression different from evaluating a numerical expression? 382
3 Name Share and Show MATH BOARD 1. Evaluate 5k + 6 for k = 4. Substitute 4 for k. Multiply. Add Evaluate the expression for the given value of the variable. 2. m 9 for m = b for b = 4 4. p for p = 6 5. The formula A = lw gives the area A of a rectangle with length l and width w. What is the area in square feet of a United States flag with a length of 12 feet and a width of 8 feet? On Your Own Math Talk MATHEMATICAL PRACTICES 8 Use Repeated Reasoning What information do you need to evaluate an algebraic expression? Practice: Copy and Solve Evaluate the expression for the given value of the variable. 6. 7s + 5 for s = d for d = 5 8. (t 6) 2 for t = (2v 3) for v = ( k 2 2) for k = (f 32) 9 for f = DEEPER The formula P = 4s gives the perimeter P of a square with side length s. How much greater is the perimeter of a square with a side length of 5 1 inches than a square with a side length of 5 inches? 2 Chapter 7 Lesson 5 383
4 MATHEMATICAL PRACTICES COMMUNICA E CONSTRUCT ARGUMENTS The table shows how much a company charges for skateboard wheels. Each pack of 8 wheels costs $50. Shipping costs $7 for any order. Use the table for Complete the table. 14. A skateboard club has $200 to spend on new wheels this year. What is the greatest number of packs of wheels the club can order? Costs for Skateboard Wheels Packs 50 n + 7 Cost $ MATHEMATICAL PRACTICE 1 Make Sense of Problems A sporting goods store placed an order for 12 packs of wheels on the first day of each month last year. How much did the sporting goods store spend on these orders last year? SMARTER What s the Error? Bob used these steps to evaluate 3m 3 3 for m = 8. Explain his error = = 21 3 = 7 WRITE Math Show Your Work 17. SMARTER The surface area of a cube can be found by using the formula 6 s 2, where s represents the length of the side of the cube. The surface area of a cube that has a side length of 3 meters is ,916 meters squared. Image Credits: (t) Comstock/Getty Images 384
5 Name Evaluate Algebraic Expressions and Formulas Evaluate the expression for the given values of the variables. Practice and Homework Lesson 7.5 COMMON CORE STANDARD 6.EE.A.2c Apply and extend previous understandings of arithmetic to algebraic expressions. 1. w + 6 for w = c for c = 7 3. b 2 4 for b = (h 3) 2 for h = 5 5. m + 2m + 3 for m = (21 3h) for h = m 9n for m = 7 and n = 5 8. d 2 9k + 3 for d = 10 and k = x + 4y 2 for x = 7 and y = 10 Problem Solving 10. The formula P = 2l + 2w gives the perimeter P of a rectangular room with length l and width w. A rectangular living room is 26 feet long and 21 feet wide. What is the perimeter of the room? 11. The formula c = 5(f 32) 9 gives the Celsius temperature in c degrees for a Fahrenheit temperature of f degrees. What is the Celsius temperature for a Fahrenheit temperature of 122 degrees? 12. WRITE Math Explain how the terms variable, algebraic expression, and evaluate are related. Chapter 7 385
6 Lesson Check (6.EE.A.2c) 1. When Debbie baby-sits, she charges $5 to go to the house plus $8 for every hour she is there. The expression 5 + 8h gives the amount she charges. How much will she charge to baby-sit for 5 hours? TEST PREP 2. The formula to find the cost C of a square sheet of glass is C = 25s 2 where s represents the length of a side in feet. How much will Ricardo pay for a square sheet of glass that is 3 feet on each side? Spiral Review (6.NS.A.1, 6. RP.A.3c, 6.EE.A.1) 3. Evaluate using the order of operations Patricia scored 80% on a math test. She missed 4 problems. How many problems were on the test? 5. What is the value of 7 3? 6. James and his friends ordered b hamburgers that cost $4 each and f fruit cups that cost $3 each. Write an algebraic expression for the total cost of their purchases. 386 FOR MORE PRACTICE GO TO THE Personal Math Trainer
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