Objectives Translate between words and algebra. Evaluate algebraic expressions.

A variable is a letter used to represent a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic expression may contain variables, constants, and operations.

Minus, difference, less than You will need to translate between algebraic expressions and words to be successful in math. + –   Plus, sum, increased by Minus, difference, less than Times, product Divided by, quotient

These expressions all mean “2 times y”: 2y 2(y) 2•y (2)(y) 2 y (2)y Writing Math

Check It Out! Example 1 Give two ways to write each algebra expression in words. 1a. 4 - n 1b. 4 decreased by n the quotient of t and 5 n less than 4 t divided by 5 1c. 9 + q 1d. 3(h) the sum of 9 and q the product of 3 and h 3 times h q added to 9

Example 2A: Translating from Words to Algebra John types 62 words per minute. Write an expression for the number of words he types in m minutes.

Example 2B: Translating from Words to Algebra Roberto is 4 years older than Emily, who is y years old. Write an expression for Roberto’s age

Example 2C: Translating from Words to Algebra Joey earns $5 for each car he washes. Write an expression for the number of cars Joey must wash to earn d dollars. Solving a literal equation—Write c in terms of d.

Check It Out! Example 2a Lou drives at 65 mi/h. Write an expression for the number of miles that Lou drives in t hours.

To evaluate an expression is to find its value. Substitute numbers for the variables and simplify.

Example 3: Evaluating Algebraic Expression Evaluate each expression for a = 4, b =7, and c = 2. A. b – c B. ac

Example 4a: Recycling Application Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. Write an expression for the number of bottles needed to make s sleeping bags.

Find the number of bottles needed to make 20, 50, and 325 sleeping bags. s 85s 20 50 325 85(20) = 1700 85(50) = 4250 85(325) = 27,625

PRACTICE AND PROBLEM SOLVING, PAGES 9–11 17. the product of 5 and p; 5 groups of p 18. 4 decreased by y; the difference of 4 and y 19. the sum of 3 and x; 3 increased by x 20. the product of 3 and y; 3 times y 21. negative 3 times s; the product of negative 3 and s 22. the quotient of r and 5; one-fifth r 23. 14 decreased by t; the difference of 14 and t 24. the sum of x and 0.5; x increased by 0.5 25. t + 20 26. 8n 27. 6 - 5 = 1 28. 5 + 3 = 8 29. 6 ÷ 3 = 2 30. 5 · 6 = 30 31a. h - 40 b. h - 40 (40) - 40 = 0 (44) - 40 = 0 (48) - 40 = 0 (52) - 40 = 0

32. To evaluate an expression is to find its value. To do this, substitute values for the variables and perform all the indicated operations. 33. 2x; possible answer: Jim has twice as many aunts as Carly, who has x aunts. 34. 17 - b; possible answer: Sarah started with 17 apples, but lost b of them. 35. y + 10; possible answer; April had y CDs and then got 10 more. 36a. air pressure b. depth below the water in feet. c. 14.7 + 0.445d = 14.7 + 0.445(8) = 14.7 + 3.56 = 18.26 psi 38a. P = 2 + 2w b. P = 2 + 2w = 2(14) + 2(8) = 28 + 16 = 44 cm c. A = · w or w d. A = w = (8)(14) = 112 cm 2 40. x 10x 1 10(1) = 10 5 10(5) = 50 10 10(10) = 100 15 10(15) = 150 44. Both algebraic and numerical expressions contain numbers and operations, but algebraic expressions also contain variables. TEST PREP, PAGE 11 48. C; b fever than 3. 49. F; 12 - 5 50. B; Sarah’s has driven the difference of 25 and x. CHALLENGE AND EXTEND, PAGE 11 51. 2ab = 2(6)(3)= 36 52. 2x + y = 2(4) + (5) = 13

SPIRAL REVIEW, PAGE 11 55. 180° - (45° + 90°) = 45° 56. 180° - (120° + 40°) = 40° 57. 180° - (30° + 60°) = 90° 58. 25% = 25/100 = 1/4 59. 50% = 50/100 = 1/2 60. 75% = 75/100= 3/4 61. 100% = 100/100= 1 62. add 8 to the previous term; 36, 44, 52 63. multiply the previous term by 3; 729, 2187, 6561 64. Add 1 to the previous term, then add 2, and then add 3, and so on; 17, 23, 30.